Question

(ii) Find the common difference of an AP whose first term is 5
and the sum of the first four terms is half the sum of the next
four terms.
​

Answer 1

Explanation:

We have

Radius of the cone =r

1

=1cm

Height of the cone =h

1

=1cm

Radius of the hemisphere =r

2

=1cm

$volume \: of \: cone \: = \binom{4}{3} \pi {r}^{2} h$

Answer 2

Answer:

Explanation:

Let d is common difference of AP

Now first 4 terms are 5, 5+d, 5+2d, 5+3d

and next 4 terms 5+4d, 5+5d, 5+6d, 5+7d

Given that, the sum of its first four terms is half the sum of the next four terms.

i.e.,

5 + 5+d + 5+2d + 5+3d=

2

5+4d + 5+5d + 5+6d + 5+7d

​

20+6d=

2

(20+22d)

​

20+6d=10+11d

d=2

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