Question

In an A.P., the first term is 25, nth term is -17 and the sum of n terms is 132. Find n and the common difference.

Answer 1

The number of terms is  12 and common difference is - 3

Step-by-step explanation:

Given :  

First term, a = 22, nth term, an (l) = - 11 and Sn = 66

By using the formula ,Sum of nth terms , Sn = n/2[a + l]

66 = n/2 [22 + (-11)]

66 × 2 = n [22 - 11]

132 = n × 11

n = 132/11

n = 12

Number of terms, n = 12

By using the formula ,an = a + (n - 1)d

-11 = 22 + (12 – 1) d

-11= 22 + 11d

-11 – 22 = 11d

-33 = 11 d

d = -33/11

d = -3

Common Difference ,d = - 3  

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

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