Question

the nth term of the A P. 63,65,67,69___and the AP 3,10, ,17, 24.. . are the value of n is ?​

Answer 1

$\bf\underline{Question:}$

The nth term of the A P. 63, 65, 67, 69,... and the AP 3, 10, 17, 24,... are equal then the value of n is ?

$\bf\underline{Answer:}$

The value of n is 13.

$\bf\underline{Explanation:}$

The first AP : 63, 65, 67, 69,...

Here, a = 63 and d = 65-63 = 2

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

$= 63 + (n - 1)2$

The second AP : 3, 10, 17, 24,...

Here a = 3 and d = 10-3 = 7

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

$= 3 + (n - 1)7$

Given, both nth terms are equal.

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

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

$60 = 7n - 7 - 2n + 2$

$65 = 5n$ ; $n = 13$

Therefore the value of n is 13.