Question

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

Answer 1

Answer:

-33 or 33

Step-by-step 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:

$a + 6d = 11a + 110d$

$11a - a = 6d - 110d$

$10a = - 104d$

$\frac{a}{d} = - \frac{104}{10}$

$\frac{a}{d} = - \frac{52}{5}$

We must have a=-52 and d=5

Or

a=52 and d=-5

For the first case, the 18th term is :

$- 52 + 5 \times 17 = 33$

For the second case,

$52 - 5 \times17 = - 33$