In an A.P. the first term is 22, nth term is -11 and the sum of first

1.	In an A.P. the first term is 22, nth term is -11 and the sum of first n term is 66. Find n and the d, the common difference.
Answer» Given, The first term of the A.P (a) = 22 The nth term of the A.P (l) = -11 And, sum of all the terms S_n = 66 Let the common difference of the A.P. be d. So, finding the number of terms by 66 = (\(\frac{n}{2}\))[22 + (−11)] 66 = (\(\frac{n}{2}\))[22 − 11] (66)(2) = n(11) 6 × 2 = n n = 12 Now, for finding d We know that, l = a + (n – 1)d – 11 = 22 + (12 – 1)d -11 = 22 + 11d 11d = – 33 d = – 3 Hence, the number of terms is n = 12 and the common difference d = -3

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

Answer»

Given,

The first term of the A.P (a) = 22

The nth term of the A.P (l) = -11

And, sum of all the terms S_n = 66

Let the common difference of the A.P. be d.

So, finding the number of terms by

66 = (\(\frac{n}{2}\))[22 + (−11)]

66 = (\(\frac{n}{2}\))[22 − 11]

(66)(2) = n(11)

6 × 2 = n

n = 12

Now, for finding d

We know that, l = a + (n – 1)d

– 11 = 22 + (12 – 1)d

-11 = 22 + 11d

11d = – 33

d = – 3

Hence, the number of terms is n = 12 and the common difference d = -3