Question

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

Answer 1

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Answer 2

Given, first term a = 22.

Given, nth term[(a + n - 1) * d] = -11.     --------- (1)

Now,

We know that Sum of n terms of an AP sn = (n/2)[2a + (n - 1) * d]

⇒ 66 = (n/2)[a + a + (n - 1) * d]

⇒ 132 = n[22 - 11]

⇒ 132 = n[11]

⇒ n = 12.

Now,

We know that nth term of an AP is an = a + (n - 1) * d

⇒ -11 = 22 + (12 - 1) * d

⇒ -11 = 22 + 11 * d

⇒ -33 = 11d

⇒ d = -3.

Therefore, the number of terms is 12 and common difference is -3.

Hope this helps!