Question

if five times the 5th term of an A.P. is equal to eight times its 8th term , then show that its 13th term is zero .

Answer 1

Answer:

Step-by-step explanation:

let of the AP

first term= a

common difference=d

ATQ

5[a+(5-1)d]=8[a+(8-1)d]

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

5a + 20d = 8a + 56d

3a = 36d

a= -12d

Now 13th term

a+(13-1)d

=-12d+12d

=0

(proved)

Answer 2

First term be a

Common difference be d

By the Information

5th term of an A.P. is equal to eight times its 8th term

Hence

5[a + (5 -1 )d] = 8[a + (8 - 1)d]

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

5a + 20d = 8a + 56d

3a = 36d

a = -12d

Hence 13th term :-

a + (13 - 1)d

= -12d + 12d

= 0

Solved