Question

if the sum of n terms of an ap is 2n2 +5n then find its second term

Answer 1

Sum of first two terms of the AP
S2=
${2n}^{2} + 5n \\ = 2( {2)}^{2} + 5 \times 2 \\ = 8 + 10 \\ = 18$
Sum of first term of AP
S1
$= 2 {n}^{2} + 5n \\ = 2 \times {1}^{2} + 5 \times 1 \\ = 2 + 5 \\ = 7$
Second term of the AP
= S2-S 1
=18-7
=11

Answer 2

The second term of the AP = 11

Given :

The sum of n terms of an AP is 2n² + 5n

To find :

The second term of the AP

Solution :

Step 1 of 2 :

Write down the given sum

Here it is given that the sum of n terms of an AP is 2n² + 5n

Sₙ = 2n² + 5n

Step 2 of 2 :

Find second term of the AP

Putting n = 1 , 2 we get

S₁ = 2 × 1² + 5 × 1 = 2 + 5 = 7

∴ First term = 7

S₂ = 2 × 2² + 5 × 2 = 8 + 10 = 18

∴ First term + Second term = 18

⇒ 7 + Second term = 18

⇒ Second term = 18 - 7

⇒ Second term = 11

The second term of the AP = 11

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