The sum of 5th and 9th …
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Posted by Sushant Thareja 6 years, 11 months ago
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Gaurav Seth 6 years, 11 months ago
The sum of 5th and 9th term is 30.
⇒ a + 4d + a + 8d = 30
⇒ 2a + 12d = 30 ..................(1)
And,
Its 25th term is 3 times its 8th term.
⇒ a + 24d = 3(a + 7d)
⇒ a + 24d = 3a + 21d
⇒ a + 24d - 3a - 21d = 0
⇒ - 2a + 3d = 0 ...................(2)
Adding equation (1) and (2).
⇒ 2a +12d = 30
- 2a + 3d = 0
________________
15d = 30
________________
⇒ 15d = 30
⇒ d = 30/15
⇒ d = 2
So, common difference, 'd' is 2.
Putting the value of d = 2 in the equation (1).
2a + 12d = 30
⇒ 2a + (12*2) = 30
⇒ 2a = 24 = 30
⇒ 2a = 30 - 24
⇒ 2a = 6
⇒ a = 6/2
⇒ a = 3
So, the first term of the required AP is 3
So, the required AP is 3, 5, 7, 9, 11, 13, 15, 19,.............
4Thank You