Book Online Demo

Check Your IQ

Try Test

Courses

Offline Centres

If the 9th term of an AP is zero, prove that its 29th term is twice its 19th term.

State true (T) or false (F).

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

True

False

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Given

a 9 = 0

.
Now deriving the equation in terms of a and d. Substitute n = 9 and

a 9 = 0

a n = a + n − 1 d

0 = a + 9 − 1 d 0 = a + 8 d a = − 8 d

And for

a 19

,n = 19 and a =

− 8 d

a n = a + n − 1 d

a 19 = − 8 d + 19 − 1 d = − 8 d + 18 d = 10 d

And for

a 29

, n = 29 and a =

− 8 d

a n = a + n − 1 d

a 29 = − 8 d + 29 − 1 d = − 8 d + 28 d = 20 d

Now let’s use 10d for

a 19

and 20d for

a 29

to prove the equation

a 29 = 2 a 19

a 29 = 2 a 19 20 d = 2 10 d 20 d = 20 d

Hence, LHS = RHS.
Therefore, the statement, “If the 9th term of an AP is zero, prove that its 29th term is twice its 19th term” is proved to be true.

Watch 3-min video & get full concept clarity