Question

The sum of first 20 terms of A. p is 400 and the sum of first 40 terms is 1600 find the sum of first 10th term​

Answer 1

Answer:

Sum of first 10 terms of AP will be 100

Step-by-step explanation:

As given ,

→ Sum of first 20 terms of AP = 400

→ S₂₀ = 400

Using formula

Sₙ = n ( 2 a + ( n - 1 ) d / 2

→ 20( 2 a + (20 -1) d ) / 2 = 400

→ 10 ( 2 a + 19 d ) = 400

→ 2 a + 19 d = 40  ... eqn (1)

Also given ,

→ Sum of first 40 terms = 1600

→ S₄₀ = 1600

Using formula

Sₙ = n ( 2 a + ( n - 1 ) d ) / 2

→ 40 ( 2 a + ( 40 - 1 ) d ) / 2 = 1600

→ 20 ( 2 a + 39 d ) = 1600

→ 2 a + 39 d = 80  .... eqn (2)

Subtracting eqn (1) from eqn (2)

⇨ 2 a + 39 d - ( 2 a + 19 d ) = 80 - 40

⇨ 2 a + 39 d - 2 a - 19 d = 40

⇨ 20 d = 40

⇨ d = 2

putting d = 2 in eqn (1)

⇨ 2 a + 19 d = 40

⇨ 2 a + 19 ( 2 ) = 40

⇨ 2 a + 38 = 40

⇨ 2 a = 2

⇨ a = 1

Now,

Finding the sum of first 10 terms

→ S₁₀  = 10 ( 2 a + ( 10 - 1 ) d ) / 2

→ S₁₀ = 5 ( 2 (1) + 9 (2) )

→ S₁₀ = 5 ( 2 + 18 )

→ S₁₀ = 5 ( 20 )

→ S₁₀ = 100

Therefore,

Sum of first 10 terms of corresponding AP will be 100 .