Question

find the sum of arithmetic progression 2 + 7 upon 2 + 5 + 13/2 ....... 10term​

Answer 1

The sum of 10 terms is $\frac{175}{2}$.

Step-by-step explanation:

The arithmetic progression is:

$2+\frac{7}{2}+5+\frac{13}{2}+...$

The sum of first n terms of an AP is:

$S_{n}=\frac{n}{2}[2a+(n-1)d]$

There are n = 10 terms in the AP.

The first term is, a = 2.

The common difference is, d = $\frac{3}{2}$.

Compute the sum of first 10 terms as follows:

$S_{n}=\frac{n}{2}[2a+(n-1)d]$

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

     $=5[4+(9\times\frac{3}{2})]$

     $=5[4+\frac{27}{2}]$

     $=5[\frac{8+27}{2}]$

     $=5\times \frac{35}{2}$

     $=\frac{175}{2}$

Thus, the sum of 10 terms is $\frac{175}{2}$.