The 24th term of an AP is twice its 10th term. Show that its 72nd term is 4 times its 15th term.

Home » The 24th term of an AP is twice its 10th term. Show that its 72nd term is 4 times its 15th term.

The 24th term of an AP is twice its 10th term. Show that its 72nd term is 4 times its 15th term.

Solution:

Suppose that a is the first term and d is the common difference of the AP. Then, we have:

$\frac{{{a}_{72}}}{{{a}_{15}}}=\frac{5d+71d}{5d+14d}$

$\frac{{{a}_{72}}}{{{a}_{15}}}=\frac{76d}{19d}=4$

${{a}_{72}}=4{{a}_{15}}$

$Hence,\text{ }the\text{ }72nd\text{ }term\text{ }of\text{ }the\text{ }AP\text{ }is\text{ }4\text{ }times\text{ }its\text{ }15th\text{ }term.$

i

Sign up now and study all subjects for free