Question

Find the value of the middle most term (s) of the AP :-11, -7, -3,..., 49 .​

Answer 1

Solution:

$\sf{Here, \: a = -11 ; d = -7 - (-11) = 4 \: and \: a_n = 49}$

$\sf{Now, \: a_n=49} \\ \longrightarrow\sf{ a+(n-1)d=49} \\ \longrightarrow \sf{4n-15=49} \\ \longrightarrow \sf{4n=49+15} \\ \longrightarrow \sf{4n=64} \\ \longrightarrow \sf{n=16}$

Here, n = 16, an even number.

$\sf{ \therefore \: Middle \: terms \: are \: \bigg[ \frac{16}{2} }\bigg]th \: term \: and \: \bigg[ \frac{16}{2} +1\bigg]th \: term$

$\sf{ \longrightarrow}8th \: term \: and \: term.$

$\sf{ Now,{a_8=a+(8-1)d=-11+7(4)=-11+28=17}} \\ \sf{And, \: a_9=a+(9-1)d=-11+8(4)=-11+32=21}$