Question

Answer the above mentioned question​

Answer 1

Question:

In an AP the sum of first n terms is 3n²/2 + 13n/2. Find the 25th terms

Answer:

We know that

nth term of an AP aₙ = Sₙ - Sₙ ₋ ₁

We have to find 25th term

So, substituting n = 25 in the formula

⇒ a₂₅= S₂₅ - S₂₅ ₋ ₁

⇒ a₂₅ = S₂₅ - S₂₄

Given Sₙ = ( 3n² + 13n ) / 2

⇒ a₂₅ = ( 3( 25 )² + 13( 25 ) ) / 2 - ( 3( 24 )² + 13( 24 ) ) / 2

⇒ a₂₅ = ( 3( 625 ) + 325 ) / 2 - ( 3( 576 ) + 312 ) / 2

⇒ a₂₅ = ( 1875 + 325 ) / 2 - ( 1728 + 312 ) / 2

⇒ a₂₅ = 2200 / 2 - 2040 / 2

⇒ a₂₅ = 1100 - 1020

⇒ a₂₅ = 80

Therefore 25th term of the AP is 80.