Question

If the sum of n terms of an AP is 3n^2+ 5n then which of its term is 164​

Answer 1

Answer:-

Given:

Sum of first n terms of an AP = 3n² + 5n

We know that,

Sum of first n terms of an AP = n/2 * [ a + l ]

Where,

• a = first term
• l = nth term or last term.

Substitute the value of n as 1 to find the sum of first 1 terms (first term)

⟶ S₁ = a = 3(1)² + 5(1)

⟶ a = 3 + 5

⟶ a = 8

Hence,

⟶ n/2 * [ 8 + l ] = 3n² + 5n

⟶ 8 + l = n(3n + 5) * (2/n)

⟶ 8 + l = 6n + 10

⟶ l = 6n + 10 - 8

⟶ l = 6n + 2

Now,

We have to find which term is 164.

We have: l = 6n + 2

So,

⟶ 6n + 2 = 164

⟶ 6n = 164 - 2

⟶ 6n = 162

⟶ n = 162/6

⟶ n = 27

Therefore, 164 is the 27th term of the given AP.