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Find the sum of 23 terms of the AP

Question:

Find the sum of 23 terms of the AP $17,12,7,2,-3, \ldots$

 

Solution:

To Find: The sum of 25 terms of the given AP series.

Sum of n terms of an AP with first term a and common difference d is given by

$S=\frac{n}{2}[2 a+(n-1) d]$

Here, a = 17, n = 23 and d = - 5

$S=\frac{23}{2}[34+22(-5)]$

$\Rightarrow S=\frac{23}{2}[34-110]=\frac{23}{2} \times(-76)$

$=-874$

Sum of 23 terms of the AP IS – 874.

 

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