The sum of 5th and 9th terms of an A.P. is 30. If its 25th term is three times its 8th term, find the A.P.
Answers
Answered by
31
Answer:
The required AP is 3, 5, 7, 9, 11, 13, 15, .............
Step-by-step explanation:
Given :
a5 + a9 = 30 and a25 = 3(a8)
Case :1
a5 + a9 = 30
By using the formula , nth term ,an = a + (n -1)d
⇒a + (5 - 1)d + a + (9 - 1)d = 30
⇒ a + 4d + a + 8d = 30
⇒ 2a + 12d = 30 ..................(1)
Case 2 :
a25 = 3(a8)
a + (25 - 1)d = 3(a + (8 - 1)d)
⇒ a + 24d = 3(a + 7d)
⇒ a + 24d = 3a + 21d
⇒ a + 24d - 3a - 21d = 0
⇒ - 2a + 3d = 0 ...................(2)
On adding equation (1) and (2),
⇒ 2a +12d = 30
- 2a + 3d = 0
-------------------------
15d = 30
⇒ d = 30/15
⇒ d = 2
common difference, 'd' = 2
On putting the value of d = 2 in the eq (1),
2a + 12d = 30
⇒ 2a + 12(2) = 30
⇒ 2a + 24 = 30
⇒ 2a = 30 - 24
⇒ 2a = 6
⇒ a = 6/2
⇒ a = 3
first term ,a = 3
Therefore, the required AP is a ,a + d , a + 2d , a + 3d , a + 4d ……
Hence, the required AP is 3, 5, 7, 9, 11, 13, 15, 19,.............
HOPE THIS ANSWER WILL HELP YOU...
Answered by
13
Step-by-step explanation:
hope it is helpful to you
Attachments:
Similar questions