# 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. - Mathematics

Sum

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.

#### Solution

First-term a = 25

nth term = -17 => last term l = -17

Sum of n terms = 132

=> n/2 [a + l] = 132

=> n(25 - 17) = 264

=> n xx 8 = 264

=> n = 33

Now l = -17

=> a + (n - 1)d = -17

=> 25 + 32d = -17

=> 32d = -42

=> d = -42/32

=> d = -21/16

Concept: Arithmetic Progression - Finding Sum of Their First ‘N’ Terms.
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#### APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 10 Arithmetic Progression
Exercise 10 (C) | Q 10 | Page 144