Find the ratio

Algebra Level 3

S 1 S_1 represents the sum of an arithmetic progression of n n odd number of terms and S 2 S_2 is the sum of the terms of the series in odd places , then what is S 1 S 2 \dfrac{S_1}{S_2} ?

n+1/n n+1/2n 2n/n+1 n/n+1

Aårÿañ Dêwâñ by Aårÿañ Dêwâñ , 21, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Sonveer Yadav
Mar 12, 2016

let 'a' be the first term and 'l' last term of the sequence.
then, S 1 S_1 = n × [ 2 a + ( n − 1 ) d ] 2 \frac {n×[2a+(n-1)d]}{2} = n × ( a + l ) 2 \frac {n×(a+l)}{2} . since, [l=a+(n-1)d]
as n is a odd number so,there will be n + 1 2 \frac {n+1}{2} odd place terms
So, S 2 S_2 = ( n + 1 ) × [ a + l ] 2 \frac {(n+1)×[a+l]}{2}

S 1 S 2 \frac {S_1}{S_2} = 2 n n + 1 \frac {2n}{n+1}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Nice solution! :D

Aårÿañ Dêwâñ - 5 years, 3 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...