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Question
In an AP, the first term is 22, nth terms is -11 and sum of first n terms is 66. Find the n and hence find the4 common difference.
Solution
Here, a = 22, Tn =-11 and sn = 66
Let d be the common difference of the given AP.
Then . Tn = -11
⇒ a+(n-1) d = 22 +(n-1) d =-11
⇒ (n-1) d = -33 ...............(i)
The sum of n terms of an AP is given by
`s_n = n/2 [ 2a +(n-1) d ] = 66` [Substituting the value off (n-1)d from (i)]
` ⇒ n/2 [ 2 xx 22 + (-33) ] = (n/2 ) xx 11 = 66`
⇒ n= 12
Putting the value of n in (i), we get:
11d = -33
⇒ d= -3
Thus, n = 12 and d = - 3
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