Multiple choice

For what value of n, is the nth term of two sequence 53, 55, 57, ... and 1, 5, 9, 13, ... equal?

  1. 25

  2. 26

  3. 27

  4. 28
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Sequence 1: a = 53, d = 2. n-th term = 53 + (n-1)2 = 51 + 2n. Sequence 2: a = 1, d = 4. n-th term = 1 + (n-1)4 = 4n - 3. Set them equal: 51 + 2n = 4n - 3. 54 = 2n, so n = 27.

AI explanation

The nth term of an arithmetic progression is given by a + (n - 1)d. For the first sequence, the formula is 53 + (n - 1) x 2, which simplifies to 2n + 51. For the second sequence, the formula is 1 + (n - 1) x 4, which simplifies to 4n - 3. Setting them equal gives 2n + 51 = 4n - 3, meaning n is 27.

Keep practicing — related questions