Question

if five times the fifth term of an ap is equal to a times its eight times in eight term. Show that its 13th term is zero

Answer 1

Answer:

Step-by-step explanation:

We know that,

5th term of AP = a + 4d

8th term of AP = a + 7d

13th term of AP = a + 12d

According to given condition ,

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

5a + 20d = 8a + 56d

8a - 5a + 56d - 20d = 0

3a + 36d = 0

Dividing by 3 on both sides,

a + 12d = 0

But 13th term is a + 12d

So, the 13th term of an AP is zero.

Hence proved

HOPE IT HELPS YOU!!

Answer 2

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

hope it helps you...................