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For whatvalue of n, are the n+n terms of two A.P's 63,65,67,..

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For whatvalue of n, are the n+n terms of two A.P's $63, 65, 67, ....... an d 3, 10, 17, ........ e q u a l$ ?

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For whatvalue of n, are the n+n terms of two A.P's

63, 65, 67, ....... an d 3, 10, 17, ........ e q u a l

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Text solutionVerified

As we know that

n^{t h}

term in an A.P. is given as-

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

Therefore,

For A.P.

63, 65, 67, .....

First term

(a) = 63

Common difference

(d) = 65 - 63 = 2

a_{n} = 63 + (n - 1) d

For A.P.

3, 10, 17, .....

First term

(A) = 3

Common difference

(d) = 10 - 3 = 7

a_{n} = 3 + (n - 1) 7

Given that:-

a_{n} = A_{n}

63 + (n - 1) 2 = 3 + (n - 1) 7

\Rightarrow 5 (n - 1) = 60

\Rightarrow n - 1 = \frac{60}{5}

\Rightarrow n = 12 + 1 = 13

Hence the

13^{t h}

term of both A.P.'s will be equal.

Hence the correct answer is

13

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Question Text	For whatvalue of n, are the n+n terms of two A.P's $63, 65, 67, ....... an d 3, 10, 17, ........ e q u a l$ ?
Answer Type	Text solution:1
Upvotes	150