Multiple choice

If 7 times the 7th term of an AP is equal to 11 times the 11th term, then its 18th term will be

  1. 7

  2. 11

  3. 18

  4. 0
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

7 (a + 6d) = 11 (a + 10d) $\Rightarrow$ 7a + 42d = 11a + 110d 7a - 11a = 110d - 42d $\Rightarrow$ -4a = 68d -a = 17d $\Rightarrow$ a = -17d Hence, a18 = a + 17d  a18 = -17d + 17d = 0.

AI explanation

In an AP, the nth term is a+(n–1)d. Setting 7(a+6d) = 11(a+10d) and simplifying gives 7a+42d = 11a+110d, or –4a = 68d, so a = –17d. The 18th term is a+17d = –17d+17d = 0, showing this specific relationship between the 7th and 11th terms forces the 18th term to vanish.

Keep practicing — related questions