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For what value of n the n^{th} term of the following two A.P.s

Question

For what value of $n$ the $n^{t h}$ term of the following two $A . P . s$ are equal?

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Owen Discussed

For what value of

n

the

n^{t h}

term of the following two

A . P . s

are equal?

9 mins ago

Discuss this question LIVE

9 mins ago

Text solutionVerified

Let

I^{s t} A . P . 63, 65, 67.........

We know that

a = 63 d = 2

a_{n} = a + (n - 1) d = 63 + (n - 1) 2 = 63 + 2 n - 2 = 2 n + 61

Let

2^{n d}

A.P. is

3, 10, 17........

a = 3, d = 7

a_{n} = a + (n - 1) d = 3 + (n - 1) 7 = 3 + 7 n - 7 = 7 n - 4 I^{s t} A . P . = 2^{n d} A . P . 61 + 2 n = 7 n - 4 61 + 4 = 7 n - 2 n 65 = 5 n n = 13

Hence, this is the answer.

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Question Text	For what value of $n$ the $n^{t h}$ term of the following two $A . P . s$ are equal?
Answer Type	Text solution:1
Upvotes	150