What is the sum of the arithmetic sequence 8, 14, 20 …, if there are 24 terms?

Solution:

We know that the sum of the first n terms of an arithmetic sequence then the n^th term is known as

s_n = n/2[2a + (n - 1)d]

where a = the first term, d = common difference and n = the number of terms.

It is given that the arithmetic sequence is 8, 14, 20 …,

First term a = 8,

Common difference d = a₂ - a₁

= 14 - 8

d = 6

Number of terms(n) = 24

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

Substituting the values, we get

S₂₄ = (24/2)[2(8) + (24 - 1)(6)]

By further calculation,

S₂₄ = 12[16 + 23 × 6] 

S₂₄ = 12(154)

S₂₄ = 1848

Therefore, the sum is S₂₄ = 1848.

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What is the sum of the arithmetic sequence 8, 14, 20 …, if there are 24 terms?

Summary:

The sum of the arithmetic sequence 8, 14, 20 …, if there are 24 terms is S₂₄ = 1848.