Question

The first three terms of an arithmetic sequence are 8, 9, 10, What's the sum of the first ten terms of the series?A) 94B) 143C) 125D) 108

Answer 1

Answer:

The sum of the first ten terms of the AP is;

$S_{10}=125$

Explanation:

Given the arithmetic sequence;

$8,9,10,\ldots$

The first term is;

$a=8$

The common difference is;

$\begin{gathered} d=9-8 \\ d=1 \end{gathered}$

Recall that the sum of n terms of an AP can be calculated using the formula;

$S_n=\frac{n}{2}(2a+(n-1)d)$

For the first ten terms;

$n=10$

Substituting the given values;

$\begin{gathered} S_{10}=\frac{10}{2}(2(8)+(10-1)1) \\ S_{10}=5(16+9) \\ S_{10}=5(25) \\ S_{10}=125 \end{gathered}$

Therefore, the sum of the first ten terms of the AP is;

$S_{10}=125$