Question : The first term of an arithmetic progression is 22 and the last term is –11. If the sum is 66, the number of terms in the sequence is:
Option 1: 10
Option 2: 12
Option 3: 9
Option 4: 8
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Correct Answer: 12
Solution :
Let the first term as $a$, the last term as $l$, and the number of terms as $n$.
Given: $a$ = 22, $l$ = –11
The sum of an arithmetic progression is given by
$S = \frac{n}{2}(a + l)$
⇒ 66 = $\frac{n}{2}$(22 – 11)
$\therefore n$ = 12
Hence, the correct answer is 12.
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