The sum of first 20 terms of an AP is 400 and sum of first 40 terms is 1600. Find the sum of its first 10 terms

Let the first term of AP be ‘a’.

Let the common difference of AP be ‘a’.

We know, sum of ‘n’ terms of an AP is

Now, Given

Sum of first 20 terms, S₂₀ = 400

⇒ 10(2a + 19d) = 400

⇒ 2a + 19d = 40 ……[1]

Also, Sum of first 40 terms, S₄₀ = 1600

⇒ 2a + 39d = 80 ……[2]

On subtracting [1] from [2]

2a + 39d – (2a + 19d) = 80 – 40

⇒ 20d = 40

⇒ d = 2

Putting this value of ‘d’ in [1],

⇒ 2a + 19(2) = 40

⇒ 2a + 38 = 40

⇒ 2a = 2

⇒ a = 1

Therefore,

Sum of first ten terms,

⇒ S₁₀ = 5(2 + 18)

⇒ S₁₀ = 100