Question

The sum of 'r' term of an ap is 2r²+3r. the nth term is.

Answer 1

GIVEN :-

The sum of 'r' term of an A.P. is 2r² + 3r.

$\sf{S_r=2r^2+3r}$

TO FIND :-

The nth term.

SOLUTION :-

$\sf{S_r=2r^2+3r}$

$\sf{\implies S_1=a_1=2(1)^2+3(1)=2+3=5}$

$\sf{\implies S_2=a_2+a_1=2(2)^2+3(2)=8+6=14}\\\\\sf{\implies a_1+a_2=14}\\\\\sf{\implies 5+a_2=14}\\\\\sf{\implies a_2=9}$

$\rule{120}1$

Common difference(d) = a₂ - a₁

⇒d = 9 - 5

⇒d = 4

$\rule{120}1$

$\sf{a_n=a+(n-1)d}\\\\\sf{\implies a_n=5+(n-1)4}\\\\\sf{\implies a_n=5+4n-4}\\\\\boxed{\sf{\implies a_n=4n+1}}$

Therefore, the value of the nth term is 4n + 1.

Answer 2

Answer:

4n+1

Step-by-step explanation:

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