Question

Write the sum using summation notation, assuming the suggested pattern continues.

-10 - 2 + 6 + 14 + ... + 110

Answer 1

is that -10 - 2 + 6 + 14 ... + 110 @aga3t

Answer 2

I'm not sure, the + before the ... was in the original problem

Answer 3

Note that the first term is -10 and last is 110 and the terms are increasing by 8. Firstly, we need to know how many terms are in this arithmetic sequence (yes this is an arithmetic sequence since it increases by the same amount each term). We need to know this because that will allow us to to choose the upper bound when we get to the summation notation. Now, to find the number of terms, we first define this arithmetic sequence using:\[\bf a_n=a+(n-1)d\]Where 'a' is the first term, 'n' is the term number, and 'd' is the common difference. For us, a = -10 and d = 8, hence we get:\[\bf a_n=-10+(n-1)8\]Since our sequence ends at 110, we must check the term number or 'n' of 110. We do so by equating the expression with 110 and solve for 'n':\[\bf 110=-10+(n-1)8 \implies 120=8n-8 \implies 128=8n \implies n = 16\]Hence we start from the first term, i.e. \(\bf n=1\) and end at \(\bf n=16\). Now the summation notation is given in the following format:\[\bf \sum_{k=1}^{n}a_k=a_1+a_2+a_3+a_4+...+a_n\]We are adding up the terms given by the sequence \(\bf -10+(n-1)d\). Can you come up with the notation for it now?

Answer 4

@aga3t

Answer 5

\[\sum_{n=0}^{\infty} (-10+8n)\]?

Answer 6

@genius12