Question

Use sigma notation to write the series -1+2+5+8+11... for 10 terms

Answer 1

Answer:
`\displaystyle \sum_(n=1)^(10) (3n-4)`

============================================

Step-by-step explanation:

This is an arithmetic sequence

`a_1 = -1` is the first term

`d = 3` is the common difference as we add 3 to each term to get the next term (eg: -1+3 = 2, or 2+3 = 5, or 5+3 = 8, etc)

let's find the nth term

`a_n = a_1 + d(n-1)\\\\a_n = -1 + 3(n-1)\\\\a_n = -1 + 3n-3\\\\a_n = 3n-4\\`

Therefore, we are summing terms of the form 3n-4 from n = 1 to n = 10

With sigma notation, we would write

`\displaystyle \sum_(n=1)^(10) (3n-4)`

This is a shorthand way to write out adding -1+2+5+8+11+...+26 where 26 is the tenth term. You would plug n = 10 into 3n-4 to get 26 as the tenth term.