Question

if the 9 term of an ap is zero then show that 29​

Answer 1

Answer:

answer is twice 19

Step-by-step explanation:

It is given that the 9

th

term of an A.P is T

9

=0

We know that the general term of an arithmetic progression with first term a and common difference d is T

n

=a+(n−1)d, therefore, the 9

th

, 19

th

and 29

th

terms are as follows:

T

9

=a+(9−1)d=a+8d.......(1)

T

19

=a+(19−1)d=a+18d......(2)

T

29

=a+(29−1)d=a+28d.......(3)

Now since T

9

=0, therefore, equation 1 becomes

0=a+8d

⇒a=−8d........(4)

Substitute the value of equation (4) in equation (3):

T

29

=−8d+28d=20d=2(10d)=2(−8d+18d)=2(a+18d)=2[T

19

] (Using equations 1 and 2)

Hence, the 29th term of A.P is twice the 19 term.

Answer 2

Answer:

The term is 0.

Step-by-step explanation:

Substituting n = 9 in this formula.

20d = 2(10d). 20d = 20d.

Therefore it is proved that 29th term is twice the 19th term when the 9th term is 0.

HOPE THIS WILL HELP YOU.

THANKS