Question

sum of 5th and 7 th term of ap is 30 if its 25 th term is 3times its 8th term find ap.....

Answer 1

Hey mate ^_^

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Answer:
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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
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           15d = 30
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⇒ 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,........

#Be Brainly❤️

Answer 2

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Given:. Sum of {5}^{th} and {7}^{th} term of AP = 30

a+4d+a+6d=30

2a+10d=30_______(1)

Given that {25}^{th} term is three times of {3}^{rd} term

${25}^{th} term = 3( {8}^{th} term)$
a+ 24d=3(a+7d)
a+ 24d= 3a+ 21d
24d- 21d= 3a- a
3d= 2a ________(2)

By putting the value 2d in equation (1) we get

2a+ 10d= 30
3d+ 10d =30
13d= 30

d= 2.3

2a = 3d
2a= 3×2.3
2a= 6.9
$a = \frac{6.9}{2}$

a= 3.45
a= 3.5

Therefore, AP is
3.5
(3.5+2.3). =5.8
(5.8+2.3) =8.1
(8.1+2.3). = 10.4

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