the 8th term of an A.P is equal to three times its third term.if its 6th term is 22, find the a.p
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let the first term be a
common difference = d
8th term is 3 times the 3rd term
(a+7d) = 3×(a+2d)
⇒ a + 7d = 3a + 6d
⇒ 7d - 6d = 3a -a
⇒d = 2a
6th term = 22
⇒a + 5d = 22
⇒a + 5×2a = 22
⇒ 11a = 22
⇒a = 22/11 = 2
d = 2a = 2×2 = 4
So first term is 2 and common difference is 4.
So the AP is 2,6,10,14,18....
common difference = d
8th term is 3 times the 3rd term
(a+7d) = 3×(a+2d)
⇒ a + 7d = 3a + 6d
⇒ 7d - 6d = 3a -a
⇒d = 2a
6th term = 22
⇒a + 5d = 22
⇒a + 5×2a = 22
⇒ 11a = 22
⇒a = 22/11 = 2
d = 2a = 2×2 = 4
So first term is 2 and common difference is 4.
So the AP is 2,6,10,14,18....
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