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Arithmetic sequence calculator

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This online tool can help you find nth term and the sum of the first n terms of an arithmetic progression. Also, this calculator can be used to solve much more complicated problems. For example, the calculator can find the common difference (d) if a5 = 19 and S7 = 105. The main advantage of this calculator is that it will generate all the work with detailed explanation.

Tutorial

What is an arithmetic sequence?

An arithmetic progression is a list of numbers in which the difference between any two successive members is a constant.

Example 1: The sequence of numbers 2, 5, 7, 10, 13,... is arithmetic because the difference between any two consecutive numbers is equal to 3.

Example 2: The sequence 2, 3, 5, 8,... is not arithmetic because the difference between terms is not constant.

Arithmetic sequence notation

a1
-
the first term of a sequence
d
-
common difference
an
-
n - th term of a sequence
Sn
-
sum of first n terms

Example 3: In the previous sequence, 2, 5, 7, 10, 13,... we have a1 = 2, d = 3, a3= 7, S4 = 24.

Arithmetic sequence formulas

d = a2 - a1
an = a1 + (n-1)d
Sn = n/2 [ 2a1 + (n-1)d]
Sn = n/2 [ a1 + an ]

Worked examples

Example 4: Find the 7-th element of an arithmetic sequence with d = 3 and a1 = 5.

an = a1 + (n-1)d
a7 = 5 + (7-1)3
a7 = 5 + 6·3
a7 = 5 + 18
a7 = 23

Example 5: Find the sum of first 10 elements of a sequence { 5, 9, 13, 17, 21,...}.

In this example we have a1 = 5, d = 4, and n = 10 since we want to sum up the first n terms.

Sn = n/2[2a1+(n+1)d]
a10 = 10/2[2*5+(10+1)4]
a10 = 5[10+11*4]
a10 = 5[10+44]
a10 = 5[54]
a10 = 108

Arithmetic Sequence Calculator
Find n - th term and the sum of the first n terms.
help ↓↓ examples ↓↓
an (the n-th term)
Sn (the sum of the first n terms )
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Get Widget Code

Arithmetic Sequence Calculator
Use this one if you need to find either a1 or d.
help ↓↓ examples ↓↓

Enter values in two out of four rows.

Arithmetic Sequence Calculator
This calc will find unknown number of terms.
help ↓↓ examples ↓↓

Enter values in three out of four rows.

Examples
ex 1:
1 + 2 + 3 + 4 + . . . + 98 + 99 + 100 = ?
ex 2:
The first term of an arithmetic sequence is equal to 5/2 and the common difference is equal to 2. Find the value of the 20th term
ex 3:
An arithmetic sequence has a common difference equal to 7 and its 8th term is equal to 43. Find its first term.?
ex 5:
The first term of an arithmetic progression is -12, and the common difference is 3 determine how many terms must be added together to give a sum of 1104.?
Find more worked-out examples in our database of solved problems.
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