What is the sum of the arithmetic sequence 6, 14, 22 …, if there are 26 terms?

Solution:

The arithmetic sequence formula is used for the calculation of the nth term of an arithmetic progression.

The arithmetic sequence is the sequence where the common difference remains constant between any two successive terms.

The sum of n terms when n^th term is unknown can be found using the formula.

S_n = n/2[2a + (n − 1)d]

Given:

Arithmetic sequence 6, 14, 22 …26 terms.

⇒ a = 6

d = 14 - 6 = 8

⇒ n = 26

Now by substituting these values on the formula, we get

S₂₆ = 26/2 [2(6) + (26−1)8]

By further calculation, we get

S₂₆ = 13[12 + (25)8]

So we get,

S₂₆ = 13[12 + 200]

S₂₆ = 13[212]

S₂₆ = 2756

Therefore, the sum of the arithmetic sequence is 2756.

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What is the sum of the arithmetic sequence 6, 14, 22 …, if there are 26 terms?

Summary:

The sum of the arithmetic sequence 6, 14, 22 …, if there are 26 terms is 2756.