Question

Sum in sigma notation and find the sum of each series 150+140+130+120+110+100

Answer 1

we are given

$150+140+130+120+110+100$

first term is 150

so,

$a_1=150$

now, we can find common difference

$d=140-150$

$d=-10$

now, we can find nth term

$a_n=a_1+(n-1)d$

$a_n=150+(n-1)*-10$

$a_n=-10n+160$

we can see that

total number of terms is 6

so, we can write it in sigma form as

$\sum _{n=1}^6\:\left(-10n+160\right)$

now, we can find sum

$sum=750$.............Answer