Question

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

Answer 1

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

Answer 2

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!