we are given
[tex] 150+140+130+120+110+100 [/tex]
first term is 150
so,
[tex] a_1=150 [/tex]
now, we can find common difference
[tex] d=140-150 [/tex]
[tex] d=-10 [/tex]
now, we can find nth term
[tex] a_n=a_1+(n-1)d [/tex]
[tex] a_n=150+(n-1)*-10 [/tex]
[tex] a_n=-10n+160 [/tex]
we can see that
total number of terms is 6
so, we can write it in sigma form as
[tex] \sum _{n=1}^6\:\left(-10n+160\right) [/tex]
now, we can find sum
[tex] sum=750 [/tex].............Answer
