In an AP, the first term is 22, nth term is -11, and sum of first n terms is 66. Find the number of terms n and the common difference d.

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Solution

Here,
$a = 22, l = - 11, S_{n} = 66$
Therefore,
$S_{n} = \frac{n}{2} (a + l) = 66$

$\frac{11 n}{2} = 66$

$n = 12$
Now, last term, $l = a + (n - 1) d = - 11$
$22 + 11 d = - 11$
$d = - 3$
Therefore, number of terms of the AP is 12 and the common difference is -3.

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In an AP, the first term is 22, nth term is -11, and sum of first n terms is 66. Find the number of terms n and the common difference d.

Here,a=22,l=−11,Sn=66Therefore,Sn=n2(a+l)=6611n2=66n=12Now, last term, l=a+(n−1)d=−1122+11d=−11d=−3Therefore, number of terms of the AP is 12 and the common difference is -3.

Here,
$a = 22, l = - 11, S_{n} = 66$
Therefore,
$S_{n} = \frac{n}{2} (a + l) = 66$

$\frac{11 n}{2} = 66$

$n = 12$
Now, last term, $l = a + (n - 1) d = - 11$
$22 + 11 d = - 11$
$d = - 3$
Therefore, number of terms of the AP is 12 and the common difference is -3.