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Sum of four consecutive terms of an AP is 50 and fourth term is four times the first find the AP

Posted by ????? ❤️ 6 years, 10 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 6 years, 10 months ago

Let the 4 numbers are a , a + d , a + 2d , a + 3d.
Sum of 4 numbers AP = 50
a + a + d + a + 2d + a + 3d = 50
⇒ 4a + 6d = 50
⇒ 2a + 3d = 25 --------------(1)
Also given the forth term is four times the first
4(a) = a + 3d
4a - a = 3d
a = d
putting a = d in (1) , we obtain
5d = 25
d = 5
a = 5 but d = a.
∴ First four terms are 5 , 10 ,15 , 20.

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