Question

Find the common difference of an A.P. whose first term is 5

and the sum of its first four terms is half the sum of its next four

terms.Find three numbers in A.P. whose sum is 15 and whose product

is 105.​
​

Answer 1

Step-by-step explanation:

Let d be the common difference of given A.P.

First term (a)=5

Given:-

a

1

+a

2

+a

3

+a

4

=

2

1

(a

5

+a

6

+a

7

+a

8

)

⇒a+(a+d)+(a+2d)+(a+3d)=

2

1

[(a+4d)+(a+5d)+(a+6d)+(a+7d)]

⇒4a+6d=

2

1

(4a+22d)

⇒4a+6d=2a+11d

⇒11d−6d=4a−2a

⇒d=

5

2×5

=2

Hence the common difference of given A.P. is 2.