Question

pls tell how to find ​

Answer 1

A.P: 6,13,20, - - - - - - - 216.

Here,

$\sf{ \boxed{ \sf{a_1 = 6}} ~~~~~~~ \boxed{ \sf{d = 13-6= 7}} ~~~~~~~ \boxed{ \sf{a_n = 216}}}$

We know

$\\ \: \: \: \sf{a_n = a+(n-1)d }$

$\: \: \: \sf{216 = 6+(n-1)7 }$

$\: \: \: \sf{216 - 6 = 7n - 7}$

$\: \: \: \sf{ 7n = 210 + 7}$

$\: \: \: \sf{ n = 217 \div 7}$

$\: \: \: \sf{ n =31}$

Total Number of term in A.P is 31.

$\sf{Middle \: term(Median) of \: A.P = \left( \frac{n+1}{2}\right)^{th} observations}$

$\sf{Middle \: term(Median) of \: A.P = \left( \frac{31+1}{2}\right)^{th} observations}$

$\sf{Middle \: term(Median) of \: A.P = \left( \frac{32}{2}\right)^{th} observations}$

$\sf{Middle \: term(Median) of \: A.P = 16^{th} \: observations}$

$\: \: \: \: \: \sf{a_{16} = a +{(16-1)} d}$

$\: \: \: \: \: \sf{a_{16} = 6 +15 \times 7}$

$\: \: \: \: \: \sf{a_{16} = 6 +105}$

$\: \: \: \: \: \sf{a_{16} = 111}$

• Hence, the middle term of the AP is 111.

Answer 2

the middle term of the AP is 111