Question

in an ap the first term is 22 nth term is -11and the sum to first n terms is 66 find n and d the common differnce

Answer 1

Given, a= 22, an = -11 and Sn = 66
We know that, a to the n=a+(n-1)d
an=a+(n−1)d
⇒ -11 = 22 +(n -1) d
⇒  (n -1)d = -11 – 22
⇒  (n -1)d = -33 ……….(1)
Also, we know that Sn = n/2[ 2a + (n -1)d]
⇒ 66 = n/2[2(22) + (n -1) d]
⇒ 132 = n[ 44 + (n -1)d]
⇒ 132 = n[ 44 -33]      [Using (1)]
⇒ 132 = n(11)
⇒ n = 12
On putting n = 12 in (1), we get
(12 -1)d = -33
⇒ 11d = -33
⇒ d = -3