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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