Find the 17th term of the arithmetic sequence calculator

Algebra 1 Algebra

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Arithmetic sequence
Nth Term Calculator
What is an arithmetic sequence?
Arithmetic sequence formula
Finding nth term, arithmetic sequence and its sum
What is the 17th term in the arithmetic?
What is the nth term of the arithmetic sequence calculator?
What is arithmetic calculator?

Emma R.

asked • 10/16/19

an= 77 + (n-1)(-5)

a. 162

b. -3

c. -8

d. 157

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1 Expert Answer

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Adrian G. answered • 10/16/19

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N represents the any number you want to find. Because you are wanting to find the 17th term or number, you will replace n = 17 into your equation.

a17 = 77 + (17-1)(-5)

a17 = 77 + (16)(-5)

a17 = 77 - 80

a17 = -3

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This online calculator can solve arithmetic sequences problems. Currently, it can help you with the two common types of problems:

Find the n-th term of an arithmetic sequence given m-th term and the common difference. Example problem: An arithmetic sequence has a common difference equal to 10, and its 5-th term is equal to 52. Find its 15-th term.
Find the n-th term of an arithmetic sequence given i-th term and j-th term. Example problem: An arithmetic sequence has its 5-th term equal to 12 and its 15-th term equal to 52. Find its 20-th term.

Some formulas and descriptions of the solutions can be found below the calculator.

Arithmetic sequence calculator and problems solver

Problem type

Find term by another term and common difference

Find term by two another terms

First Term of the Arithmetic Sequence

nth Term of the Sequence Formula

Arithmetic sequence

To recall, an arithmetic sequence or arithmetic progression (AP) is a sequence of numbers such that the difference, named common difference, of two successive members of the sequence, is a constant.

Thus, the formula for the n-th term is

and in general

where d is the common difference.

You can solve the first type of problems listed above by using the general formula directly or calculating the first term a1, using the formula.

And then using the formula for the n-th term.

For the second type of problem, you need to find common difference using the following formula derived from the general formula.

After that, it becomes the first type of problem.

The calculator above also calculates the first term and general formula for the n-th term of an arithmetic sequence for convenience.

Enter the values in the below input boxes to calculate the nth term and sum of arithmetic progression by using arithmetic sequence/series calculator.

Nth Term Calculator

Arithmetic sequence calculator is an online tool that calculates:

Arithmetic Sequence
Nth term value
Sum of arithmetic sequence

What is an arithmetic sequence?

Arithmetic sequence can be defined as,

“An arithmetic sequence is a sequence where each term increases by adding or subtracting some constant value known as common difference (d).”

Arithmetic sequence is commonly known as arithmetic series and arithmetic progression as well.

Arithmetic sequence formula

Formula to find nth term is:

nth term = a + (n - 1)d

Formula to find sum of arithmetic progression is:

S = n/2 × [2a₁ + (n - 1)d]

Where:

a refers to nᵗʰ term of the sequence,
d refers to common difference, and
a₁ refers to first term of the sequence.

There is no specific formula to find arithmetic sequence. In the next section, we will explain the method to calculate arithmetic sequence using common difference and first term.

Finding nth term, arithmetic sequence and its sum

For the calculation of nth term, arithmetic sequence and its sum, you can simply use the arithmetic series calculator above.

Example:

Find the nth term and sum of arithmetic sequence for 15 number of terms if first term is 5 and difference is 4.

Solution:

Step 1:Identify the values.

n = 15

a = 5

d = 4

Step 2:Use arithmetic sequence formula and place the values.

For finding the nth term

nth term = a + (n - 1)d

= 5 + (15 - 1) × 4

= 61

nth term = 61

For finding the sum of arithmetic sequence

S = n/2 × [2a₁ + (n - 1)d]

S = 15/2 × [2(5) + (15 - 1) × 4]

S = 495

For finding the Arithmetic Sequence

Add common difference in the first term to get the arithmetic sequence. Keep adding the common difference in the preceding number till you get last number in the sequence.

a1 = 5

a2 = a1 + d = 5 + 4 = 9

a3 = a2 + d = 9 + 4 = 13

a4 = a3 + d = 13 + 4 = 17

a5 = a4 + d = 17 + 4 = 21

a6 = a5 + d = 21 + 4 = 25

a7 = a6 + d = 25 + 4 = 29

a8 = a7 + d = 29 + 4 = 33

a9 = a8 + d = 33 + 4 = 37

a10 = a9 + d = 37 + 4 = 41

a11 = a10 + d = 41 + 4 = 45

a12 = a11 + d = 45 + 4 = 49

a13 = a12 + d = 49 + 4 = 53

a14 = a13 + d = 53 + 4 = 57

a15 = a14 + d = 57 + 4 = 61

Arithmetic Sequence = 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61

Use the arithmetic progression calculator above to verify the value of nth term and arithmetic sequence.

What is the 17th term in the arithmetic?

Detailed Solution Hence, 17th term is 67. Download Soln PDF. Share on Whatsapp. Latest DSSSB TGT Updates. Last updated on Oct 19, 2022.

What is the nth term of the arithmetic sequence calculator?

For an arithmetic sequence, the nth term is calculated using the formula s + d x (n - 1). So the 5-th term of a sequence starting with 1 and with a difference (step) of 2, will be: 1 + 2 x (5 - 1) = 1 + 2 x 4 = 9. For a geometric sequence, the nth term is calculated using the formula s x s⁽ⁿ ^- ¹⁾.

What is arithmetic calculator?

A calculator is a device that performs arithmetic operations on numbers. Basic calculators can do only addition, subtraction, multiplication and division mathematical calculations.