Question

Find the sum of the series : 3+5+7+6+9+13+17+... to 3n terms.

Answer 1

The given sequence i.e.,$3+5+7+6+9+12+9+13+17+......to3n$.

can be written as $3+6+9+....to10terms+5+9+13+...to10terms+7+12+17+....10terms$.

hence the required sum is$=\frac{10}{2}$

$=[2\times 3+(10-1\left)3\right]+\frac{10}{2}$

$=[2\times 5+(10-1\left)4\right]+\frac{10}{2}$

$=[2\times 7+(10-1\left)\right]5$

$=5(6+9\times 3)+5(10+9\times 4)+5(14+9\times 5)$

$=5(6+27+10+36+14+45)$

$=5\times 138$

$=690$