Find the 4th term of an AP, if the sum of first n terms is 2n2 + 3n1.

1.	Find the 4th term of an AP, if the sum of first n terms is 2n2 + 3n1. 412. 423. 604. None of these
Answer» Correct Answer - Option 4 : None of these Concept: If series is in AP then nth term of AP = a_n= S_n- S_{(n - 1)} Calculations: Given series is in AP and the sum of first n terms is 2n2 + 3n ⇒ S_n=2n2 + 3n. Then, the first term will be when n=1 in the above expression ⇒ S1 = 2 + 3 = 5 Sum of first two terms, n = 2 , S₂= 2 × 2² + 3 × 2 = 14 So, the second term will be a₂= S₂- S₁= 14 - 5 = 9 Similarly, n = 3, S3 = 2 × 3² + 3 × 3 = 27 So, the third term will be a3 = S3 - S₂ = 27 - 14 = 13 Similarly, n = 4, S4 = 2 × 4² + 3 × 4 = 44 So, the fourth term will be a4 = S4 - S3 = 44 - 27 = 17 Hence, the 4th term of an AP is 17.

Find the 4th term of an AP, if the sum of first n terms is 2n2 + 3n1. 412. 423. 604. None of these

Answer» Correct Answer - Option 4 : None of these

Concept:

If series is in AP then nth term of AP = a_n= S_n- S_{(n - 1)}

Calculations:

Given series is in AP and the sum of first n terms is 2n2 + 3n

⇒ S_n=2n2 + 3n.

Then, the first term will be when n=1 in the above expression

⇒ S1 = 2 + 3 = 5

Sum of first two terms,

n = 2 , S₂= 2 × 2² + 3 × 2 = 14

So, the second term will be

a₂= S₂- S₁= 14 - 5 = 9

Similarly,

n = 3, S3 = 2 × 3² + 3 × 3 = 27

So, the third term will be

a3 = S3 - S₂ = 27 - 14 = 13

Similarly,

n = 4, S4 = 2 × 4² + 3 × 4 = 44

So, the fourth term will be

a4 = S4 - S3 = 44 - 27 = 17

Hence, the 4th term of an AP is 17.

Discussion

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