Question

what is the sum of first n terms of an AP is(3n²+5n), Which term of this AP is 152​

Answer 1

25th term. 

is answer

Step-by-step explanation:

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Answer 2

Given:

The sum of the first "n" terms of AP is (3n² + 5n)  

To find:

In which AP term 152 contain.

Solution:

The given term (3n² + 5n)

Substitute "n=1" in given term

S₁ = a₁  

⇒ 3 + 5 = 8

Substitute "n=2" in given term

S₂ = a₁ + a₂

⇒ 12 + 10 = 22

a₂ = S₂ - S₁

⇒ 22 - 8 = 16

S₃ = a₁ + a₂ +a₃

⇒ 27 + 15

= 42

a₃ = S₃ - S₂

⇒ 42 - 22 = 20

Given AP is,

8,14,20...

a = 8

d = 6

Tm = 152

152 = (8 + (n-1)6)

152 = (8+ 6n - 6)

152 = 2 + 6n

152 - 2 = 6n

150 = 6n

$\frac{150}{6}$ = n

∴ n = 25.

The AP of 152 is 25th term.