**Examples of Arithmetic Sequences Problems – ***Sinaumed’s* must be familiar with the material on Arithmetic Sequences and Series which is included in the Mathematics subject? Yep, this material generally begins to be studied in grade 11 even semester.

Arithmetic Sequences and Series material will definitely be discussed together with Geometry Sequences and Series. Even further, this material can also appear on CPNS questions , *of* course, with a higher level of difficulty. To learn it, *Sinaumed’s* can read material reviews, understanding formulas, along with examples of problems with arithmetic sequences which are usually found in problem practice books.

So, what if the examples of arithmetic sequences in practice books have already been discussed? Well, don’t worry, because in the following article we will discuss examples of arithmetic sequence problems that *Sinaumed’s* can see and do!

## 30 Examples of Essay Arithmetic Sequences

- The 40th term of sequence 7, 5, 3, 1, … is …
- The first term of the arithmetic sequence is 3 and the difference = 4, the 10th term of the arithmetic sequence is …
- Find the 100th term of the arithmetic sequence 2, 5, 8, 11, …
- Find the 21st term of the arithmetic sequence: 17, 15, 13, 11,…
- Determine the 8th and 20th terms of the sequence –3, 2, 7, 12, ….
- You know the arithmetic sequence –2, 1, 4, 7, …, 40. Find the number of terms in the sequence.
- It is known that the first term of an arithmetic sequence is 7 and the 15th term is 63. Find the difference in the arithmetic sequence!
- The first term of the arithmetic sequence is -2 and the difference is 5, determine the 12th term of the arithmetic sequence is…
- The 3rd and 16th terms of the arithmetic sequence are 13 and 78. Determine the first terms and their difference.
- The formula for the nth term of the sequence 5, –2, –9, –16, … is …
- It is known that the sequence of numbers with the nth term is of the form Un = n2 – 2n. Write down the first 5 terms of the sequence.
- Know the sequence of numbers 4, 7, 12, 19, …. Determine the formula for the nth term.
- Know the sequence of numbers 4, 7, 12, 19, …. Which term of the sequence is 199?
- The 15th term of the number sequence: 2, 5, 8, 11, 14, … is…
- The 45th term of the number sequence: 3, 7, 11, 15, 19, … is…
- The 50th term of the number sequence: 20, 17, 14, 11, 8, …. is….
- The formula for the nth term of the arithmetic sequence 94, 90, 86, 82, …. is….
- A sequence 1, 4, 7, 10, … fulfills the pattern Un = an + b. The 10th term of the sequence is
- A sequence of 2, 5, 10, 17, …. meet the pattern Un = an2 + bn + c. The 9th term of the sequence is….
- Sequences 2, 9, 18, 29, … fulfill the pattern Un = an2 + bn + c. What tribe is 42?
- The 20th term of sequence 1, 1, 1, 2, 1, 3, 1, 4, 1, …. is
- The arithmetic sequence 1, 3, 5, 7, … is known. un = 225. Determine the number of terms (n).
- Si Dadap successfully passed the PT (Higher Education) entrance examination. As a student, starting January 1, 2008 he received an allowance of Rp. 500,000.00 for one quarter. This allowance is given at the beginning of each quarter. For each subsequent quarter the pocket money he receives is increased by Rp. 25,000. How much pocket money will Dadap receive in early 2011?
- It is known that the 1st term of an arithmetic sequence is 6 and the fifth term is 18, determine the difference.
- In a theater, seats are arranged with the front row consisting of 12 seats, the second row containing 14 seats, the third row containing 16 seats, and so on. The number of seats in the 20th row is…
- The 2nd term of an arithmetic sequence is 5. If the sum of the 4th and 6th terms of the series is 28, then the 9th term is …..
- The 10th and 14th terms of an arithmetic sequence are 7 and 15, respectively. Determine the first term, difference, and 20th term of the sequence.
- You know the arithmetic sequence –2, 1, 4, 7, …, 40. Find the number of terms in the sequence.
- From an arithmetic sequence, the third term is 36, the fifth and seventh terms are 144. The first ten terms of the series are….
- The first term of a sequence is 4, while the nth general term (for n > 1) is determined by the formula Un = 3.Un–1 – 5. The 3rd term is …

## 10 Examples of Problem Arithmetic Sequences and Their Discussion

### Example Question 1

Find the 100th term of the arithmetic sequence 2, 5, 8, 11, …

**Discussion:**

a = 2

b = u2 – u1 = 5 – 2 = 3

n = 100 un = a + (n – 1)b

un = 2 + (100 – 1)3 = 2 + (99 x 3) = 299

### Example Problem 2

The arithmetic sequence 1, 3, 5, 7, … is known. un = 225. Determine the number of terms (n).

**Completion:**

a = 1, b = 2, un = 225

un = a (n – 1)b

225 = 1 + (n – 1)2 = 1 + 2n – 2

226 = 2n

n = 113

### Example Problem 3

Si Dadap successfully passed the PT (Higher Education) entrance examination. As a student, starting January 1, 2008 he received an allowance of Rp. 500,000.00 for one quarter. This allowance is given at the beginning of each quarter. For each subsequent quarter the pocket money he receives is increased by Rp. 25,000. How much pocket money will Dadap receive in early 2011?

**Completion:**

1st Quarter: u1 = a = Rp. 500,000.00

2nd quarter: u2 = a + b = Rp. 525,000.00, etc

So b = 25,000.

At the beginning of 2011, the college had been used for 3 years or 12 quarters, meaning: u12 = a + (12 – 1)b = 500,000 + (11 x 25,000) = 775,000

So the amount of money that Dadap will receive at the beginning of 2011 is Rp. 775,000.00.

### Example Problem 4

It is known that the 1st term of the arithmetic sequence is 6 and the fifth term is 18, determine the difference.

**Completion: **

It is known that a = 6, and U5 = 18

Un = a + (n – 1) b

U5 = 6 + (5 – 1) b

18= 6 + 4b

4b = 12

b = 3

So the difference is 3.

### Example Problem 5

Find the 21st term of the arithmetic sequence: 17, 15, 13, 11,…

**Completion: **

If a = 17, b = -2, and n = 21,

then U21 = 17 + (21-1)(-2) = **-23 **

So, the 21st term of the arithmetic sequence is -23

### Example Problem 6

The 40th term of sequence 7, 5, 3, 1, … is …

**Completion:**

Given: a = 7

b = –2

Asked 𝑈40 ?

Answer:

𝑈𝑛 = 𝑎 + (𝑛 − 1) 𝑏

𝑈40 = 7 + (40 − 1) (−2)

= 7 + 39 x (-2)

= 7 + (-78) = – 71

So, the 40th term of the arithmetic sequence is –71.

### Example Problem 7

The formula for the nth term of the sequence 5, –2, –9, –16, … is …

**Discussion: **

Given: a = 5 b = –7

Wanted: the formula for the nth term of the arithmetic sequence = ?

**Answer:**

𝑈𝑛 = 𝑎 + (𝑛 − 1) 𝑏

= 5 + (𝑛 − 1)(−7)

= 5 − 7 𝑛 + 7

= 12 − 7 𝑛

So, the formula for the nth term of the arithmetic sequence is 𝑈𝑛 = 12 − 7𝑛

### Example Problem 8

In a theater, seats are arranged with the front row consisting of 12 seats, the second row containing 14 seats, the third row containing 16 seats, and so on. The number of seats in the 20th row is…

**Discussion: **

Is known:

a = 12

b = 2

Asked 𝑈20 ?

**Answer:**

𝑈𝑛 = 𝑎 + (𝑛 − 1)𝑏

𝑈20 = 12 + (20 − 1)(2)

= 12 + 19 . (2)

= 12 + (38) = 50

So, the number of seats in the 20th row is 50 seats

### Example Problem 9

The 10th number of the sequence: 3, 5, 7, 9, ….is…

**Completion:**

a = 3, b = 2,

U10 = (a + 9b)

U10 = 3 + 18 = 21

### Example Problem 10

A sequence of 2, 5, 10, 17, …. meet the pattern Un = an2 + bn + c. 9th tribe of

that line is…

**Completion**

Is known :

Rows 2, 5, 10, 17, …

𝑈𝑛 = 𝑎𝑛2 + 𝑏𝑛 + 𝑐

Asked: 𝑈9 = ⋯ ?

**Answer:**

𝑈𝑛 = (1)𝑛2 + (0)𝑛 + 1

𝑈𝑛 = 𝑛2 + 1

𝑈9 = 92 + 1

𝑈9 = 82

Well, that’s a review of some examples of questions about Arithmetic sequences in Mathematics. After listening to the questions and discussion, does *Sinaumed’s* understand that sequences and series in Arithmetic are different?