If the sum of n terms of an A P is...

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If the sum of n terms of an A.P. is 3n² + 5n then which of its terms is 164 ?

A. 26^th

B. 27^th

C. 28^th

D. None of these

Answer: Option B

Solution(By Examveda Team)

Sum of n terms of an A.P. = 3n² + 5n
Let a be the first term and d be the common difference
S_n = 3n² + 5n
S₁ = 3(1)² + 5 × 1 = 3 + 5 = 8
S₂ = 3(2)² + 5 × 2 = 12 + 10 = 22
∴ First term (a) = 8
a₂ = S₂ - S₁ = 22 - 8 = 14
d = a₂ - a₁ = 14 - 8 = 6
Now a_n = a + (n - 1)d
⇒ 164 = 8 + (n - 1) × 6
⇒ 6n - 6 = 164 - 8
⇒ 6n = 156 + 6
⇒ 6n = 162
⇒ n = $$\frac{{162}}{6}$$
⇒ n = 27
∴ 168 is 27^th term

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Comments ( 1 )

Shoukatul Alam :

4 years ago

Sn=3n2+5n

S1=a1=3(1)2+5(1)=8

S2=3(2)2+5(2)=22

S2=22=a1+a2

a2=22-8=14

d=a2-a1=14-8=6

nth term value is 164,then what is n?

nth term=a+(n-1)d

164=8+(n-1)6

164-8 / 6=n-1

156/6=n-1

26+1=n

n=27

So 27thterm is 164.