# 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 - Mathematics

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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

#### Solution

In the given problem, we have the first and the nth term of an A.P. along with the sum of the n terms of A.P. Here, we need to find the number of terms and the common difference of the A.P.

Here,

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

The nth term of the A.P (l) = −11

Sum of all the terms Sn = 66

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

So, let us first find the number of the terms (n) using the formula,

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

66 = (n/2 ) (22 - 11)

( 66)(2) = (n)(11)

Further, solving for n

n =( (66)(2))/11

n = (6) (2)

n = 12

Now, to find the common difference of the A.P. we use the following formula,

l = a + ( n-1) d

We get,

-11 = 22 + ( 12 - 1) d

- 11 = 22 + ( 11) d

(-11 - 22) /11 = d

Further, solving for d,

d =( -33)/11

d = -3

Therefore, the number of terms is n = 12  and the common difference of the A.P.d = -3 .

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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 5 Arithmetic Progression
Exercise 5.6 | Q 25 | Page 52