Question

· If S = n² + 2n then find T?​

Answer 1

Answer:

-(2n+1)

Step-by-step explanation:

sn+1=n2-1

tn=sn+1-sn

=-(2n+1)

Answer 2

Solution :

Explanation :

Given,

Sum of n terms of the AP is n² + 2n

To finD

nth term

Let a be the first term and d be the common difference in the required AP

Putting n = 1,we get the first term :

$\sf S_1 = a_1 = 1^2 + 2(1) = 2$

Putting n = 2,we get the sum of first and second terms :

$\sf S_2 = a_1 + a_2 = 2^2 + 2(2) = 8$

Now,

Second Term would be :

$\sf a_2 = S_2 - a_1 \\ \\ \implies \sf a_2 = 8 - 2 \\ \\ \implies \sf a_2 = 6$

Now,

Common Difference

$\sf D = a_2 - a_1 = 6 - 2 = 4$

Nth term of an AP :

$\sf T = a + (N - 1)D \\ \\ \longrightarrow \sf T = 2 + (N - 1)4 \\ \\ \longrightarrow \sf T = 4N - 2$

Thus,the nth term of the above AP is 4N - 2