Question

• if the frist term and the common difference
of beth an Ap are given by the ratio
of volumes of a cone a cylinder of same
base radius and equal rights respective
Find the sum of 25th terms of the
Ap?​

Answer 1

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Answer 2

QUESTION:

If the first term and common difference of an AP are given by ratio of volumes of a cone and cylinder of same base radius and equal heights, respectively. Find then sum of first 25 terms of AP.

SOLUTION:

Let,

First term be 'a'

And common difference be 'd'

NOW,

Ratio of volumes of cone and cylinder whose radii are' r' and heights are 'h'

Will be

(1/3πr^2h) : πr^2h

I. E,

1 : 3 ( one ratio three)

So,

First term of A. P will be 1

a = 1

And common difference will be 3

d= 3

Sum of first n terms of AP is

Sn = n/2 (2a +(n-1) d)

We have to find sum of first 25 terms of the AP

So,

S(25) = 25/2{2(1) +(25-1) (3) }

S(25) = 25/2 ( 2 + 72)

S(25) = 25/2× 74

S(25) = 925

SO THE SUM OF FIRST 25 TERMS OF THIS AP WILL BE 925.