The sum of first 30 terms of an AP is equal to the sum of its first 20 terms. Show that the sum of the first 50 terms of the same AP is zero.
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Step-by-step explanation:
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.
Hope it helps!
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