Question

The sum oh n terms of an AP is 2n²+5n. Find the common difference

Answer 1

Hey there !!

Given :-

→ Sum of n terms [ S$\tiny n$ ] = 2n² + 5n .

To find :-

→ The common difference [ d ] .

Solution :-

We have,

→ S$\tiny n$ = 2n² + 5n .

Now taking the value of n = 1,

⇒ S₁ = 2 × (1)² + 5 × 1 .

⇒ S₁ = 2 + 5 .

⇒ S₁ = 7.

Now taking the value of n = 2,

⇒ S₂ = 2 × 2² + 5 × 2 .

⇒ S₂ = 2 × 4 + 10.

⇒ S₂ = 8 + 10.

⇒ S₂ = 18.

∵ a₁ = S₁ = 7.

And, a₂ = S₂ - S₁ .

⇒ a₂ = 18 - 7 .

∴ a₂ = 11 .

⇒ d =  a₂ - a₁ .

⇒ d = 11 - 7 .

∴ d = 4 .

Hence, it is solved .

THANKS

#BeBrainly.