Question

If 4 time the 4th term of an ap is equal to 18 time the 18th term then find the 22th term

Answer 1

4(a+3d)=18(a+17d)
or 4a+12d=18a+18*17d
or 18a-4a+306d-12d=0
or 14a+294d=0
or a+21d=0

then answer is 0......

Answer 2

✬ 22nd term = 0 ✬

Step-by-step explanation:

Given:

• 4 times the 4th term of an AP is equal to 18 times the 18th term.

To Find:

• What is the 22th term of AP?

Solution: As we know that AP is given by

★ a^n = a + ( n – 1 ) d ★

➯ 4th term of AP = a + (4 – 1)d

➯ a⁴ = a + 3d

and

➯ 18th term of AP = a + (18 – 1)d

➯ a¹⁸ = a + 17d

A/q

• 4 times the 4th term of an AP is equal to 18 times the 18th term.

$\implies{\rm }$ 4 (a + 3d) = 18 (a + 17d)

$\implies{\rm }$ 4a + 12d = 18a + 306d

$\implies{\rm }$ 4a – 18a = 306d – 12d

$\implies{\rm }$ – 14a = 294d

$\implies{\rm }$ a = 294d/–14

$\implies{\rm }$ a = – 21d....(1)

[ 22nd term of AP is given by ]

➮ a²² = a + (22 – 1)d

➮ a²² = – 21d + 21d {From equation 1}

➮ a²² = 0

Hence, the 22nd term of AP is 0.