For what value of n, are the nth terms of two APs 63, 65, 67, ...

Question.

For what value of n, are the nth terms of two APs 63, 65, 67, ... and 3, 10, 17, .... equal?


Solution:

l. Two APs are 63, 65, 67, ..., 3, 10, 17, ...

From (1), First term = 63 and common difference = 2

Its $n$th term $=63+(n-1) \times 2=2 n+61$

From $(2)$, First term $=3$ and common difference $=7$

Its nth term $=3+(n-1) \times 7=7 n-4$

Putting $7 \mathrm{n}-4=2 \mathrm{n}+61$

$\Rightarrow 7 n-2 n=61+4 \Rightarrow 5 n=65 \Rightarrow n=13$

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