Question

Help needed.

The sum of the first 10 terms of an arithmetic progression 225 . Find the sum of the next 20 terms of the progression given that the sum of the first 20 terms of the progression is 1010​

Answer 1

S = 2010

I hope it helps.

Answer 2

2130

Explanation:

AP

S₁₀= 225

S₂₀= 1010

S₁₁₋₃₀=?

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S₁₁₋₃₀= S₃₀ - S₁₀

• (1) S₁₀= 10/2(2a₁+9d) = 225 ⇒ 10a₁+45d=225

• (2) S₂₀= 20/2(2a₁+19d) = 1010 ⇒ 20a₁+190d=1010

• S₃₀= 30/2(2a₁+29d)= 30a₁+ 435d

• S₃₀ - S₁₀= 30a₁ + 435d - 10a₁ -45d= 20a₁ + 390d= 1010 + 200d

Comparing (1) and (2):

• (2)- 2*(1) ⇒ 190d- 90d= 1010-450 ⇒ 100d= 560 ⇒ 200d= 1120

S₁₁₋₃₀= 1010+1120= 2130