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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

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True

False

answer is A.

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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.

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