Question

the sum of 5 th and 9 th terms of an A.P is 30 if it's 25 th term is three times it's 8 th term find the A.P​

Answer 1

Given

The Sum of 5th and 9th term is 30

Its 25th term is three times its 8th term

To Find AP

Formula

Tₙ = a+(n-1)d

According to Question

T₅ + T₉ = 30            (i)

T₂₅ = 3(T₈)               (ii)

Take (i)

a + 4d + a + 8d = 30

2a + 12d = 30

2(a + 6d ) = 30

a + 6d = 15            (i)

a = 15 - 6d             (i)

Take (ii)

a + 24d = 3(a + 7d)         (ii)

a + 24d = 3a + 21d

3a - a + 21d - 24d = 0

2a - 3d = 0       (ii)

Now Put the value of a = 15 - 6d on (ii)

2a - 3d = 0

2(15-6d) - 3d = 0

30 - 12d -3d = 0

30 = 15d

d = 2

Put the value of d = 2 on (i) eq

a = 15 - 6d

a = 15 - 6(2)

a = 15 - 12

a = 3

Answer

Series are ; 3,5,7,9,,,,,,,,,

Answer 2

Answer:

Given :-

• The sum of 5th and 9th terms of an A.P is 30.
• It's 25th term is three times it's 8th term.

Find Out :-

• What are you A.P.

Solve :-

We know that,

❖ Tn = a + (n - 1)d ❖

Then, the equation is :

➪ T₅ + T₉ = 30 . . . . . (1)

➪ T₂₅ = 3(T₈) . . . . . . (2)

Now, from taking 1 we get,

➻ a + 4d + a + 8d = 30

➻ 2a + 12d = 30

➻ 2(a + 6d) = 30

➻ a + 6d = 30 ÷ 2

➻ a + 6d = 15

➻ a = 15 - 6d

➠ a = 15 - 6d

Now, by taking equation 2 we get,

➻ a + 24d = 3(a + 7d)

➻ a + 24d = 3a + 21d

➻ a - 3a + 24d = 21d

➻ - 2a = 21d - 24d

➻ - 2a = - 3d

➻ 2a = 3d

➻ 2a - 3d = 0

➠ 2a - 3d = 0

Now, put the value of a in equation no 2,

➻ 2a - 3d = 0

➻ 2(15 - 6d) - 3d = 0

➻ 30 - 12d - 3d = 0

➻ - 12d - 3d = - 30

➻ - 15d = - 30

➻ 15d = 30

➻ d = 30 ÷ 15

➻ d = 2

➠ d = 2

Now, put the value of d in equation 1 we get,

➻ a = 15 - 6d

➻ a = 15 - 6(2)

➻ a = 15 - 12

➻ a = 3

➠ a = 3

Hence, the series will be 3 , 5 , 7 , 9 , 11 , 13 ,,,,,,,,,