Multiple choice

If nth term of the two series 3 + 10 + 17 + .... and 63 + 65 + 67 + .... are equal, then value of n is

  1. 9

  2. 13

  3. 19

  4. More than one of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Series 1: a=3, d=7. n-th term = 3 + (n-1)7 = 7n - 4. Series 2: a=63, d=2. n-th term = 63 + (n-1)2 = 2n + 61. Setting them equal: 7n - 4 = 2n + 61 => 5n = 65 => n = 13.

AI explanation

The general formula for the nth term of an arithmetic progression is tn = a + (n - 1)d, where a is the first term and d is the common difference. For the first series, the nth term is 3 + (n - 1)7 = 7n - 4, and for the second series, the nth term is 63 + (n - 1)2 = 2n + 61. Equating the two expressions gives 7n - 4 = 2n + 61, which simplifies to 5n = 65. Solving this equation, we find that the value of n is 13.

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