Question

find the middle term of the A.P -15, -11 , -7, -3 ... 49​

Answer 1

Answer :- 9th term that is 17 .

Explanation :-

Using formula :- nth term = a + (n-1)d

where a is first term and d is common difference .

here , common difference is +4 .

so ,

=> 49 = -15 + (n-1)4

=> 64 = 4n - 4

=> n = 68/4 = 17

therefore , 49 is 17 term

hence middle term is 9th term

9th term = -15 + (9-1) ×4 = 17

Answer 2

$\tt{\red{\overline{\underline{\huge{solution}}}}}$

an = a + ( n - 1 ) d________[ 1 ]

$\mathcal{\huge{ AP = - 15 , - 11 , - 7 ..... , 49}}$

$\tt{\huge{a = - 15 }}$

$\tt{\huge{ d = 4 }}$

$\tt{\huge{ an = 49 }}$

$\tt{\huge{ n = ?}}$

So , from [ 1 ] ,

49 = - 15 + [ n - 1 ] . 4

[ n - 1 ] . 4 = 64

n - 1 = 16

$\tt{\huge{\boxed{n = 17}}}$

As , n is odd , middle term , m , is

$\tt{\huge{ m^th = [ n + 1 ] / 2 }}$

$\tt{\huge{ m^th = 18 / 2}}$

$\tt{\huge{\boxed{ m^th = 9 }}}$

Now by formula , mth term is ,

$\tt{\huge{ a9 = - 15 + [ 9 - 1 ] . 4}}$

$\tt{\huge{a9 = - 15 + 32}}$

$\tt{\huge{\boxed{ a9 = 17 }}}$

$\tt{\red{\overline{\underline{\huge{Answer = 17 }}}}}$

$<marquee> Plz Follow Me And Mark as Brainliest </marquee>$