What is the sum of the arithmetic sequence 8, 14, 20 …, if there are 22 terms?

Solution:

Given: Arithmetic sequence is 8, 14, 20, ……

The sum of first n terms of an arithmetic sequence is Sn = n/2 [2a + (n - 1)d]

From the sequence, we know

First term a = 8

Common difference d = a₂ - a₁ = 14 - 8 = 6

Number of terms n = 22

S_n = n/2[2a + (n - 1)d] --- (1)

Substituting the values in (1)

S₂₂ = 22/2[2(8) + (22 - 1)6]

S₂₂ = 11[16 + (21)6]

By further calculation

S₂₂ = 11[16 + 126]

S₂₂ = 11[142]

S₂₂ = 1562

Therefore, the sum of the arithmetic sequence is 1562.

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What is the sum of the arithmetic sequence 8, 14, 20 …, if there are 22 terms?

Summary:

The sum of the arithmetic sequence 8, 14, 20 …, if there are 22 terms is 1562.