Question

(i) Is 68 a term of the A.P. 7, 10, 13, ..... ?

(ii) Is 302 a term of the A.P. 3, 8, 13, ..... ?

Answer 1

(i) 68 a term of A.P. 7, 10, 13, ..... ?

Here, a = 7

and d = 10 - 7 = 3

$\therefore a_n$ term is $=a+(n-1)d$

$=7+(n-1)3$

Let 68 be nth term of A.P.

Then,

$68=7+3(n-1)$

$\Rightarrow 68=7+3n-3$

$\Rightarrow 68-4=3n$

$\Rightarrow 64=3n$

$\Rightarrow n=\frac{64}{3}$

Which is not a natural number.

$\therefore$ 68 is not a term of given A.P.

(ii) Is 302 a term of A.P. 3, 8, 13

and d = (8 - 3) = 5

Let 302 be nth term of the given A.P.

Here, $302=3+(n-1)5$

$\frac{299}{5}=(n-1)$

$n=\frac{304}{5}$

Which is not a natural number.

$\therefore$ 302 is not a term of given A.P.