Find the middle term of the AP 6, 13, 20, …., 216.

Home » Find the middle term of the AP 6, 13, 20, …., 216.

Find the middle term of the AP 6, 13, 20, …., 216.

Solution:

The given AP is 6, 13, 20,………..216

First term, a = 6 and the common difference d = 13 – 6 = 7

Assuming that there are n terms in the AP, we can write:

${{a}_{n}}=216$

$6+(n-1)\times 7=216$

$7(n-1)=216-6=210$

$n-1=30$

$n=31$

Thus, the number of terms in AP is 31. therefore, the middle term is:

$=\left( \frac{31+1}{2} \right)th\,term$

$=16\,th\,term$

$=6+(16-1)\times 7$

$=6+105=111$

$Hence,\text{ }the\text{ }middle\text{ }term\text{ }of\text{ }the\text{ }given\text{ }AP\text{ }is\text{ }111.\text{ }$

i

Sign up now and study all subjects for free