If 4 times the 4th term of an AP is equal to 18 times its 18th term then find its 22nd term.
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If 4 times the 4th term of an AP is equal to 18 times its 18th term then find its 22nd term.
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We know that nth term of an AP an = a + (n - 1) * d
(i)
Given that 4th term of an AP is 18 times its 18th term.
⇒ 4(a4) = 18(a18)
⇒ 4(a + 3d) = 18(a + 17d)
⇒ 4a + 12d = 18a + 306d
⇒ 4a - 18a = 306d - 12d
⇒ -14a = 294d
⇒ -14a - 294d = 0
⇒ 14a + 294d = 0
⇒ a + 21d = 0
⇒ a + (22 - 1)d = 0
⇒ a22 = 0
Therefore, the 22nd term is 0.
Hope this helps!
Verified answer
N th term of AP is given by the formula An= a +(n-1)d, where a represents first term and d represents the common difference.ATP,
A4=a+3d
A18=a+17d
4* a4 = 18* a18= 4(a+3d)= 18(a+17d)= 4a+12d = 18a+306d =>0 = 18a-4a+306d-12d= 0 = 14a+294d 0= a+21d -21d = a= a18= a +21d = (-21d)+21d=0 therfore its twenty first term is 0
I hope this will help you