Answer:
-33 or 33
Step-by-step explanation:
The seventh term of an AP is written as:
[tex]a + 6d[/tex]
The eleventh term of an AP is written as:
[tex]a + 10d[/tex]
If the 7th term is 11 times the 11th term, then;
[tex]a + 6d = 11(a + 10d)[/tex]
Expand to get:
[tex]a + 6d = 11a + 110d[/tex]
[tex]11a - a = 6d - 110d[/tex]
[tex]10a = - 104d[/tex]
[tex] \frac{a}{d} = - \frac{104}{10} [/tex]
[tex] \frac{a}{d} = - \frac{52}{5} [/tex]
We must have a=-52 and d=5
Or
a=52 and d=-5
For the first case, the 18th term is :
[tex] - 52 + 5 \times 17 = 33[/tex]
For the second case,
[tex]52 - 5 \times17 = - 33[/tex]
