Question

use summation notation to write the arithmetic series for the specified number of terms then evaluate the sum.

50+55+60+ .....; n=7

Answer 1

so for this the want you to express it as a single notation
\[\sum_{j}^{n}n _{j}\] where n=7

Answer 2

so you put n = 7 at the bottom right, but how do you do the rest

Answer 3

summation is
\[\sum_{j=50}^{7}(n _{j}+5)\]

Answer 4

so you start at 50 then add 5 for each subsequent term till you stop at 7 terms

Answer 5

I gotta go, hopefully this is helpful
If not message me and I can look at it again tomorrow

Answer 6

\[\sum_{i=0}^{6}(50+5i)\]

Using formula : -
a=50
d=5
n=7
nth term= \[a+(n-1)d\]
(replacing the variables with the actual values) we get nth term(here 7th term) as -> 50+(7-1)5=80
The sum of n terms= \[\frac{ n }{ 2}(2a+(n-1)d)\] (replacing the variables) we get the sum to be
\[\frac{ 7 }{ 2}(50\times2 + (7-1)\times5) =455\]

Therefore in this A.P.,
7th term=80
Summation of the series=455