Question

Answer the following question fast if correct get marked as brainliest​

Answer 1

Answer:

Here, the value of fifth term is 31.

Step-by-step explanation:

Here, As per our given question,

=T6+T20=79 (As given in question, that terms between T5 and T21 have total value of 79)

=Here, First term =a, Common difference=d

=T6=a+(6-1)×d

=T6=a+5d,

=T20=a+19d

Now, by putting value of both terms, we get,

=a+5d+a+19d=79

=2a+24d=79

=a+12d=79-(1st)eq. (As 2and 12 both are divisible by 2)

=Now, =T21=127

=a+20d=127-(2nd)eq.

Now by solving both equations by elimination method, we get,

=a+12d=79

=a+20d=127

As both equations have same mathematical signs, their sign would be changed on solving and we get,

=12d-20d=79-127

=(-8d)=(-48)

=8d=48 (Asinus sign is on both sides are are equal, so both minus signs would be cancelled)

=d=48/8

=d=6

Now, by putting value of d in (1st)eq. we get,

=a+12×(6)=79

=a+72=79

=a=79-72

=a=7

Now, According to question,

=Fifth term is =T5=a+(n-1)×d (where n=5, number of terms)

=T5=7+(5-1)×6

=T5=7+24

=T5=31 (Answer)

Hence, the value of fifth term in this A.P. is 31.

Thank you.