Sum of First 30 Terms of an AP

CAT 2004 Slot 1 · QA · Easy · Progressions

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If the sum of the first 1111 terms of an arithmetic progression equals that of the first 1919 terms, then what is the sum of the first 3030 terms?

  1. A.

    00

  2. B.

    −1-1

  3. C.

    11

  4. D.

    Not unique

Answer

A

Explanation

Let the AP have first term aa and common difference dd. S11=S19  ⟹  112[2a+10d]=192[2a+18d]S_{11} = S_{19} \implies \frac{11}{2}[2a + 10d] = \frac{19}{2}[2a + 18d] 22a+110d=38a+342d  ⟹  16a+232d=0  ⟹  2a+29d=022a + 110d = 38a + 342d \implies 16a + 232d = 0 \implies 2a + 29d = 0 The sum of the first 30 terms is: S30=302[2a+29d]=15×(0)=0S_{30} = \frac{30}{2}[2a + 29d] = 15 \times (0) = 0

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