Question

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

Options

• 7

• 11

• 18

• 0

Answer 1

If 7 times the 7^th term of an AP is equal to 11 times its 11^th term, then its 18^th term will be 0.

Explanation:

`7a_7 = 11a_11`

⇒ `7[a + (7 - 1)d] = 11[a + (11 - 1)d]`    ....`[because a_n = a + (n - 1)d]`

⇒ `7(a + 6d) = 11(a + 10d)`

⇒ `7a + 42d = 11a + 110d`

⇒ `4a + 68d` = 0

⇒ `2(2a + 34d)` = 0

⇒ `2a + 34d` = 0   ....[∵ 2≠ 0]

⇒ `a + 17d` = 0  ......(i)

∴ 18^th term of an AP, `a_18 = a + (18 - 1)d`

= `a + 17d` = 0   .....[From equation (i)]