Question

If five times the 5th term of an A.P.is equal to eight times it's 8th term,then show that it's 13th term is zero.​

Answer 1

Answer:

let first term of AP be= a

and common difference =d

now,

fifth term of AP can be written as=a+4d

and eight term=a+7d

ATQ....

5(a+4d)=8(a+7d)

5a+20d=8a+56d

-3a=36d

-a=12d

now,

13th term =a+12d

=-12d+12d=o

hope it works

Step-by-step explanation:

plz mark it as brainliest answer

Answer 2

Answer:

equate and solve as below

Step-by-step explanation:

to prove

13th term = 0

let 1st term be a and progression is d

5th term is a+4d

8th term is a+7d

to prove: a+12d =0

as per question:

5(a+4d)=8(a+7d)

5a+20d=8a+56d

-3a=36d

3a+36d=0

a+12d=0 which is the 13th term