Question

If the sixth term of an HP is 10 and the 11th term is 18. Find the 16th term.

• A. $80$
• B. $90$
• C. $100$
• D. $110$

Answer 1

The correct option is B $90$

Here, $a+5d=\frac{1}{10}$

And, $a+10d=\frac{1}{18}$

Solving these two equations, we get,

$a=\frac{13}{90}$ and $d=-\frac{2}{225}$

Now,

$a+15d=\frac{13}{90}-\frac{2}{15}=\frac{1}{90}$

Hence, the ${16}^{th}$ term is $90.$