Question

find the second term if the sum of nth of an AP is 2n²+5n

Answer 1

QuestioN :

Find the second term if the sum of nth of an AP is 2n²+1​

GiveN :

• AP is 2n²+ 5n

To FiNd :

• The second term

ANswer :

The second term is 4n + 3.

SolutioN :

$\sf S_n_-_1 = 2(n-1)^2+5(n-1)$

$\sf \implies 2(n^2-2n+1)+5n-5$

$\sf \implies 2n^2-4n + 2+5n-5$

$\sf \implies 2n^2+n-3$

Now,

$\sf t_n= S_n-S_n_-_1$

$\sf \implies 2n^2+5n-(2n^2+n-3)$

$\sf \implies 2n^2+5n-2n^2-n+3$

$\sf \implies 4n+3$

∴ Hence, The second term is 4n + 3.

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Answer 2

Answer:

$S_n_-_1 = 2(n-1)^2+5(n-1)$

$2(n^2-2n+1)+5n-5$

$2n^2-4n + 2+5n-5$

$2n^2+n-3$

Now,

$t_n= S_n-S_n_-_1$

$2n^2+5n-(2n^2+n-3)$

$2n^2+5n-2n^2-n+3$

$4n+3$