MBApyq

Sum of Arithmetic Progression

XAT 2015 · Quantitative Ability & Data Interpretation · Easy · Quantitative Ability

All XAT 2015 questionsMore Quantitative Ability questionsAll XAT QADI

What is the sum of the following series? −64,−66,−68,…,−100-64, -66, -68, \dots, -100

  1. A.

    -1458

  2. B.

    -1558

  3. C.

    -1568

  4. D.

    -1664

  5. E.

    None of the above

Answer

B

Explanation

The given series is an Arithmetic Progression (AP) with first term a=−64a = -64, common difference d=−2d = -2, and last term an=−100a_n = -100. an=a+(n−1)d  ⟹  −100=−64+(n−1)(−2)  ⟹  −36=−2(n−1)  ⟹  n=19a_n = a + (n-1)d \implies -100 = -64 + (n-1)(-2) \implies -36 = -2(n-1) \implies n = 19 Sum Sn=n2(a+an)=192(−64−100)=19×(−82)=−1558S_n = \frac{n}{2}(a + a_n) = \frac{19}{2}(-64 - 100) = 19 \times (-82) = -1558.

Related Quantitative Ability questions

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace