Arithmetic Sequence Calculator

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Arithmetic sequence is a sequence where the terms in the sequence follow by a common difference. The common difference is the difference between any two consecutive numbers in the sequence and is denoted by ‘d’. Arithmetic sequence calculator is the quick online tool which is useful in finding the ‘n’th term in the sequence or the sum of the sequence.

Example 1: Find the 10^th term of the sequence: 2, 5, 8, 11,……

Given sequence is arithmetic sequence because,

5 - 2 = 3 or 8 – 5 = 3

Common difference between any two consecutive numbers is 3.

So first term, a₁ = 2

Common difference, d = 3

So nth term = a + (n-1)d

10^th term n = 10

So, 10^th term = 2 + (10-1)*3

10^th term = 2 + 9 * 3 10^th term = 2 + 27 = 29

Example 2: For the above sequence: 2, 5, 8, 11, …… find the sum of the sequence till the 10^th term.

Sum of certain number of terms of an Arithmetic sequence = S_n = n/2 * (a₁ + a_n)

Given, first term, a₁ = 2

Last term, a₁₀= 29 (from the above answer)

n = 10 terms

So S_n = n/2 * (a₁ + a_n)

S₁₀ = 10/2 * (2 + 29)

S₁₀ = 5 * (31)

S₁₀ = 155

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