Question

I am having trouble converting a word problem to Sigma Notation:
Using sigma notation, describe the total length of 7 pictures hung side-by-side. Then find the total length the pictures occupy along the wall if the first picture has a length of 10 inches and the length of each successive picture is 4 inches longer than the previous one.

Answer 1

\[\sum\limits_{j=0}^610[\text{in}]+4j[\text{in}]\]
\[=\sum\limits_{j=0}^6(10+4j)[\text{in}]\]

Answer 2

Where does the 6 come from? What is the [in]?

Answer 3

Oh starting a 0, I understand the 6.

Answer 4

[in] is the units , inches

Answer 5

oh okay. Thanks for your help!

Answer 6

you could also have written this\[\sum\limits_{i=1}^710[\text{in}]+4(i-1)[\text{in}]\]\[=\sum\limits_{i=1}^7\left(10+4(i-1)\right)[\text{in}]\]
they are mathematically equivalent

Answer 7

Oh wow, I didn't even think about that. Thanks again for your help!