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The 9th term of an AP is -32 and the sum of its 11th and 13th

Question

The $9$ th term of an AP is $- 32$ and the sum of its $11$ th and $13$ th terms is $- 94$ . Find the common difference of the AP.

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Liam Discussed

The

9

th term of an AP is

- 32

and the sum of its

11

th and

13

th terms is

- 94

. Find the common difference of the AP.

14 mins ago

Discuss this question LIVE

14 mins ago

Text solutionVerified

Let

a

be the first term and

d

be the common difference of an AP.

nth term

= a_{n} = a + (n - 1) d

Given:

9

th term of an AP is

- 32

and the sum of its

11

th and

13

th terms is

- 94

Now,

a_{9} = a + 8 d = - 32

.......

(1)

a_{11} = a + 10 d

a_{13} = a + 12 d

Sum of

11

th and

13

th terms:

a_{11} + a_{13} = a + 10 d + a + 12 d

- 94 = 2 a + 22 d

a + 11 d = - 47

.........

(2)

Subtracting

(1)

from

(2)

, we have

3 d = - 47 + 32 = - 15

d = - 5

Common difference is

- 5

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Question Text	The $9$ th term of an AP is $- 32$ and the sum of its $11$ th and $13$ th terms is $- 94$ . Find the common difference of the AP.
Answer Type	Text solution:1
Upvotes	150

The 9th term of an AP is −32 and the sum of its 11th and 13th terms is −94. Find the common difference of the AP.

Text solutionVerified

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The $9$ th term of an AP is $- 32$ and the sum of its $11$ th and $13$ th terms is $- 94$ . Find the common difference of the AP.