A partial sum of an arithmetic sequence is given Find the su

A partial sum of an arithmetic sequence is given. Find the sum. -18 - 17.9 - 17.8 - ... -0.1 Determine whether the infinite geometric series is convergent or 1 - 1/3 + 1/9 - 1/27 + ...

Solution

in the partial sum

first term a =-18

common difference d =0.1

n^th term a_n =a+ d(n-1)

-18+ 0.1(n-1)=-0.1

0.1(n-1)=17.9

n-1=179

n=180

sum =(n_/2)(first term+last term)

sum =(180_/2)(-18-0.1)

sum =-1629