Question : What is the sum of the first 13 terms of an arithmetic progression if the first term is –10 and the last term is 26?
Option 1: 104
Option 2: 140
Option 3: 84
Option 4: 98
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Correct Answer: 104
Solution :
Given: The sum of the first 13 terms and the first term is –10 and the last term is 26.
By using the formula, S
n
= $\frac{n}{2}[a+l]$
Where $a$ is the first term, $l$ is the last term of the A.P., and $n$ is the number of terms.
By putting the values of 1
st
and last term, we get,
⇒ S
13
= $\frac{13}{2}$[–10 + 26]
⇒ S
13
= $\frac{13}{2}$[16]
$\therefore$ S
13
= 13 × 8 = 104
Hence, the correct answer is 104.
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