JEE Main 2020 · 7 January · evening · Single correct · +4 / −1

If the sum of the first 40 terms of the series,
3 + 4 + 8 + 9 + 13 + 14 + 18 + 19 + ..... is (102)m, then m is equal to :

  1. (a) 20
  2. (b) 5
  3. (c) 10
  4. (d) 25
Answer and solution

Answer (a) 20

Solution

Maths sir · 3 steps

The series is not an AP, but adding the terms in pairs turns it into one.

  1. Pair the terms. Group the terms two at a time: (3+4) + (8+9) + (13+14) + …. The pair sums are 7, 17, 27, …, an AP with first term 7 and common difference 10.
  2. Count the pairs. The first 40 terms make exactly 20 pairs, so you need the sum of the first 20 terms of this new AP.

    S = 20/2[2(7) + (20-1)(10)] = 10 (14 + 190) = 2040

  3. So. 102 m = 2040 gives m = 20, which is option (a).

The idea to keep. When a series grows in a repeating pattern of steps, like +1, +4, +1, +4, group the terms by one full cycle. The group sums usually form a clean AP.

Answer from the NTA final answer key. Solution by PrepWiser.

Study Sequences & Series

Asked about 250 times in JEE Main since 2020. This question is from 2020.