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

1.	In an A.P., the first term is 22, nth term is -11 and the sum to first n terms is 66. Find n and d, the common difference.
Answer» Given, First term, a = 22 n^th term, a_n= -11 = l and sum of n terms, S_n= 66 We know sum of n terms, S_n = \(\frac{n}{2}[a + l]\) 66 = \(\frac{n}{2}[22 - 11]\) 66 x 2 = n x 11 n = \(\frac{66 \times 2}{111} = 12\) we know, a_n= a + (n – 1) d -11 = 22 + (12 – 1) d -11 – 22 = 11d -33 = 11d d = -3 Hence, number of terms, n = 12 and common difference, d = -3

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

Answer»

Given,

First term, a = 22

n^th term, a_n= -11 = l

and sum of n terms, S_n= 66

We know sum of n terms, S_n = \(\frac{n}{2}[a + l]\)

66 = \(\frac{n}{2}[22 - 11]\)

66 x 2 = n x 11

n = \(\frac{66 \times 2}{111} = 12\)

we know, a_n= a + (n – 1) d -11

= 22 + (12 – 1) d -11 – 22

= 11d -33 = 11d

d = -3

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