JEE Main 2023 · 30 January · evening · Numerical answer · +4 / −0

The 8ᵗʰ common term of the series
S₁=3+7+11+15+19+… . . ; ; S₂=1+6+11+16+21+… . .
is :

Answer and solution

Answer 151

Solution

Maths sir · 3 steps

Find the first common term, then step by the LCM of the two differences to reach the 8th one.

  1. First common term. S₁ goes 3, 7, 11, … and S₂ goes 1, 6, 11, …. So the first number that appears in both is 11.
  2. Common difference. S₁ moves in steps of 4 and S₂ in steps of 5. A number stays in both only if you move by a multiple of both 4 and 5. So the common terms form an AP with first term 11 and difference LCM(4, 5) = 20: 11, 31, 51, …

    T₈ = a + (8-1)d = 11 + 7 × 20

  3. So. T₈ = 11 + 140 = 151, so the 8th common term is 151.

The common slip: 171. Using a + 8d instead of a + 7d gives 11 + 160 = 171, which is the 9th common term, not the 8th.

The idea to keep. Common terms of two APs form a new AP. Its first term is the first number the two share, and its difference is the LCM of the two differences.

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 2023.