Question

If Sn=3n2+2n, then find 10th term of A.P

Answer 1

Answer:

$\boxed{\large{\red{\bf t_{10} = 59}}}$

Step-by-step explanation:

Given that -

• Sₙ = 3n² + 2n

To find :

• 10th term of AP, i.e., t₁₀

Solution :

We know that,

• tₙ = Sₙ - Sₙ₋₁

To find 10th term, we need to find S₁₀ and S₉.

Finding S₁₀ :

⇒ Sₙ= 3n² + 2n

⇒ S₁₀ = 3 (10)² + 2 (10)

⇒ S₁₀ = 3 (100) + 20

⇒ S₁₀ = 300 + 20

⇒ S₁₀ = 320

Finding S₉ :

⇒ Sₙ= 3n² + 2n

⇒ S₉ = 3 (9)² + 2 (9)

⇒ S₉ = 3 (81) + 18

⇒ S₉ = 243 + 18

⇒ S₉ = 261

Finding t₁₀ :

⇒ tₙ = Sₙ - Sₙ₋₁

⇒ t₁₀ = S₁₀ - S₉

⇒ t₁₀ = 320 - 261

⇒ t₁₀ = 59

Hence, the 10th term of AP is 59.