Question

The sum of first n terms of an Ap is 2n^2 + n. Find nth term and common difference of the A.P.

Answer 1

AnswEr :

Sum of "n" terms in the AP is : 2n² + n

Let a and d be the first term and common difference of the AP.

Consider the expression 2n² + n

Putting n = 1,we would the get the first term of the AP :

$\sf S_1 = a_1 = 2(1)^2 + 2 \\ \\ \implies \sf a_1 = 2 + 2 \\ \\ \implies \sf a_1= 4$

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

$\sf S_2 = a_1 + a_2 = 2(2)^2 + 2 \\ \\ \implies \sf a_1 + a_2 = 2(4) + 2 \\ \\ \implies \sf a_1 + a_2 = 10 \\ \\ \implies \sf a_2 = 10 - a_1 \\ \\ \implies \sf a_2 = 10 - 4 \\ \\ \implies \sf a_2 = 6$

Common difference is the difference of two consecutive terms

Thus,

$\sf D = a_2 - a_1 \\ \\ \implies \sf D = 6 - 4 \\ \implies \boxed{\boxed{\sf D = 2 }}$

nth term of the AP :

$\star \ \boxed{\boxed{\sf a_n = a + (n - 1)D }}$

Putting the values,

$\longrightarrow \sf a_n = 4 + (n - 1)2 \\ \\ \longrightarrow \sf a_n = 4 + (n - 1)(2) \\ \\ \longrightarrow \underline{\boxed{\sf a_n = 2n + 2}}$

Answer 2

Answer:

an=2n+2 is the answer if your miss asks tell the answer

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