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Q.

State True/False.


If 4 times the 4th term of an AP is equal to 18 times its 18 th term then its 22nd term is 0.


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a

False  

b

True

answer is A.

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Detailed Solution

Given that, 4 times the 4th term of an AP is equal to 18 times its 18 th term.
According to the given condition:
4× t 4 =18× t 18 −−−−(1)
Let a be the first term and d be the common difference of the A.P.
Formula for the n th term:
t n =a+ n−1 ×d
Applying the formula of n th term of AP and calculate the 4th term. ∴ t 4 =a+(4−1)d ⇒ t 4 =a+3d−−−−−(2)
Applying the formula of n th term of AP and calculate the 18th term.      ∴ t 18 =a+(18−1)d ⇒ t 18 =a+17d−−−−−(3) Applying the formula of n th term of AP and calculate the 22th term. ∴ t 22 =a+(22−1)d−−−−−(4)
Put the value of t 4 from equation (2) and the value of t 18 from equation (3) into equation (1):
∴4(a+3d)=18(a+17d) ⇒4a+12d=18a+306d ⇒−14a=294d ⇒a=−21d
  ⇒a+21d=0 ⇒a+(22−1)d=0−−−−−(5)
Put a+(22−1)d= t 22  from equation (4) in equation (5) ,  Thus, t 22 =0 .
Therefore, 22nd term of A.P. is 0.
Thus, the given statement is true.
Hence, option (1) is correct.
 
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