Question

If the sum of first m terms of an AP is 2m*2 + 3 m, then what is its second term?
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Answer 1

Step-by-step explanation:

Given:

$S_m = 2 {m}^{2} + 3m \\ \\ \therefore \: S_1 = 2 \times {1}^{2} + 3 \times 1 \\ \\ \therefore \: S_1 = 2 \times 1 + 3 \\ \\ \therefore \: S_1 = 2 + 3 \\ \\ \therefore \: S_1 = 5 \\ \\ now \\ \\ S_2= 2 \times {2}^{2} + 3 \times 2\\ \\ \therefore \: S_2 = 2 \times 4 + 6 \\ \\ \therefore \: S_2 =8 + 6 \\ \\ \therefore \: S_2 = 14 \\ \\ \because \: t_2 = S_2 - S_1 \\ \\ \therefore \:t_2 =14 - 5\\ \\ \huge \purple{ \boxed{\therefore \:t_2 =9}}$