Question

If $\frac{1+3+5+7+.....uptonterms}{2+4+6+8+......uptonterms}=0.95$, find $n$.

Answer 1

Given that:

$2+4+6+\mathrm{8....}uptonterms=0.95(1+3+5+7+....uptonterms)$

Since both series are $A.P.$ therefore using $Sum=\frac{n}{2}[2a+(n-1\left)d\right]$ formula, we get

$\frac{n}{2}[2\times 2+2n-2]=\frac{n}{2}\times 0.95[2\times 1+2n-2]$

$2n-2=0.95\times 2n$

$0.05n=2$

$n=40$