Question

verify whether 301 is a term of the given stories 5,11,17,23,....

Answer 1

$\bf{Given}$ :- AP -: 5,11,17,23.....

$\bf{To\: prove}$ :- 301 is a term in the given AP

$\bf{Proof}$:- AP :-

5,11,17,23....

a(first term) =5

d (common difference) = second term- first term

=11-5

=6

To find if a term belongs to an AP, then 'n' should come out to be a whole number.

an=301

a+(n-1) d =301

5 +(n-1) ×6 =301

(n-1) ×6 =301-5

(n-1) ×6 = 296

n-1 =296/6

n-1 = 49.33...

n=49.33...+1

n=50.333....

Here n ≠ whole number.

So, 301 is not a term of the AP.

$\bf{Hope\:it\:helps\: :) }$