· If S = n² + 2n then find T?

1.	· If S = n² + 2n then find T?
Answer» 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

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