Question

If the 7th of an AP is equal to 11 times the 11th term, find the 18th term

Answer 1

-33 or 33

Explanation:

The seventh term of an AP is written as:

`a + 6d`

The eleventh term of an AP is written as:

`a + 10d`

If the 7th term is 11 times the 11th term, then;

`a + 6d = 11(a + 10d)`

Expand to get:

`a + 6d = 11a + 110d`

`11a - a = 6d - 110d`

`10a = - 104d`

`(a)/(d) = - (104)/(10)`

`(a)/(d) = - (52)/(5)`

We must have a=-52 and d=5

Or

a=52 and d=-5

For the first case, the 18th term is :

`- 52 + 5 * 17 = 33`

For the second case,

`52 - 5 *17 = - 33`