Question

Find the sum of two middle terms of the ap -4/3,-1,-2/3,-1/3,.....,41/3

Answer 1

Answer:

Given A.P. :

-4/3,-1,-2/3,-1/3,.....,41/3

Here,

first term, a = -4/3

Common difference, d = -1-(-4/3)

ie, d = -1+4/3

d = 1/3

Last term, T(n)=41/3

=> a+(n-1)d=41/3

=> -4/3 + (n-1)(1/3) = 41/3

=> -4+(n-1)=41

=> n-1=41+4

=> n=45-1

=> n=44.

Here , the total number of terms in the given A.P. is 44, which is a even natural number.

Thus, in this A.P. there would be two middle terms , namely (n/2)th term and

{(n/2)+1}th term.

ie, in this A.P. the two middle terms are,

22nd term and 23rd term.

we know that, the nth term of an A.P. is given as, T(n)=a+(n-1)d

thus,

T(22)=a+(22-1)d

= a+21d

and,

T(23)=a+(23-1)d

=a+22d

now,

T(22)+T(23)=a+21d + a+22d

= 2a+43d

= 2(-4/3) + 43(1/3)

= -8/3 + 43/3

= (-8+43)/3

= 35/3

thus, the required sum is 35/3