Question

if the sum of first 20 terms of A. P is equal to the sum of 30 terms, then the sum of first 50 terms is _____​

Answer 1

Answer:

Given, Sum of first 30 terms = Sum of first 20 terms.

∴ S₃₀ = S₂₀

⇒ (30/2)[2a + (30 - 1) * d] = (20/2)[2a + (20 - 1) * d]

⇒ 15[2a + 29d] = 10[2a + 19d]

⇒ 30a + 435d = 20a + 190d

⇒ 10a = -245d

⇒ a = 24.5d

Now,

Sum of first 50 terms = (50/2)[2a + (50 - 1) * d]

                                  = 25[49d + 49 * d]

                                  = 25[0]

                                  = 0.

Therefore,Sum of first 50 terms is 0.

STAN KPOP IDOLS

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