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Formula for Sum of n Terms of an AP

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Question

Find the sum of first 10 terms of the arithmetic series if $a_{1} = 25$ and $a_{10} = 100$ .

A

300

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B

320

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C

625

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D

312

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Solution

The correct option is B $625$
The sum of n terms of arithmetic sequence can be calculated by the formula $S_{n} = \frac{n}{2} (a_{1} + a_{n})$
Where is the number of terms, $a_{1}$ is the firth term and $a_{n}$ is the last term.
$n = 50$
First term $= 25$
Tenth term $= 100$
Therefore, $S_{10} = \frac{10}{2} (25 + 100)$
$= 5 (25 + 100)$
$= 5 (125)$
$= 625$
Hence, the sum of first 10 terms is $625.$

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