Question

in an A.p the sum of the 4th and the 10th terms is -14 the sum of the 6th and the 12th terms is -26 find the fifth term​

Answer 1

Answer:

-1

Step-by-step explanation:

Given:

4th term + 10th term=-14

4th term means T4

10th term T10

T4+T10= - 14---------------a

6th term means T6

12th term means T12

T6+T12=-26-----------------b

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

a-first term in the series

d=common difference

Apply thus formula for T4, T10, T6, T12

T4=a+3d

T10=a+9d

T6=a+5d

T12=a+11d

Substitute all this in equations

Eq (a) becomes a+3d+a+9d=. - 14

2a+12d=. - 14-------------c

Eq(b) becomes a+5d+a+11d=. - 26

2a+16d= - 26-------------d

Subtract this (c) eq and (d) eq

2a+12d=. - 14

2a+16d=. - 26

0a-4d=-14+26

-4d=12

d=-3

common diff is d=-3

substitute d in any one of the eq to get a value

2a+12(-3)=. - 14

2a-36= - 14

2a=22

a=11

Now we have a and d value to find 5th term we hav formula

T5=a+(n-1)d

Substitute a and d

T5=11+4(-3)

T5=11-12

T5=-1

5th term is - 1