Which cylinders have the same volume as the cylinder below? Check all that apply. A cylinder with height of 32 meters and diamet
2 answers:
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Answer : <em>The</em><em> </em><em>required</em><em> </em><em>ratio</em><em> </em><em>is</em><em> </em><em>(</em><em>1</em><em>4</em><em>m</em><em>-</em><em>6</em><em>)</em><em>:</em><em>(</em><em>8</em><em>m</em><em>+</em><em>2</em><em>3</em><em>)</em><em> </em><em>.</em>
Here we are given that the ratio of sum of first n terms of two AP's is (7n + 1):(4n + 27) .
That is.
As , we know that the sum of n terms of an AP is given by ,
Assume that ,
- First term of 1st AP = a
- First term of 2nd AP = a'
- Common difference of 1st AP = d
- Common difference of 2nd AP = d'
Using this we have ,
Now also we know that the nth term of an AP is given by ,
Therefore,
From equation (i) and (iii) ,
Substitute this value in equation (i) ,
Simplify,
From equation (ii) ,