A store displays seven computers on a shelf side-by-side. Find the total length of the computers on the table if the first computer was six inches wide and the width of each successive computer is three inches longer than the previous one.

Show all your work and describe the sigma notation used in answering the question above

Question

A store displays seven computers on a shelf side-by-side. Find the total length of the computers on the table if the first computer was six inches wide and the width of each successive computer is three inches longer than the previous one.

Show all your work and describe the sigma notation used in answering the question above

anonymous · Answer

1st computer=6"
each next is 3" longer so
2nd computer=6+3=9"
3rd=9+3=12"
4th=12+3=15"
5th=15+3=18"
6th=18+3=21"
7th=21+3=24"

now to find the total length add them up all...as

=6+9+12+15+18+21+24=105

anonymous · Answer

whats the sigma notation

ganeshie8 · Answer

6, 9, 12,...

what type of sequence is this ?

anonymous · Answer

arthmetic sequence

ganeshie8 · Answer

yes, can you write the general term ?
also called `nth term`

anonymous · Answer

n=1

anonymous · Answer

upper index=7

anonymous · Answer

3n+3(middle)

ganeshie8 · Answer

first term, $\large  a_1 =  6$
common difference, $\large   d=3$
nth term, $\large a_n =  ?$

anonymous · Answer

6+(n-1)3

ganeshie8 · Answer

$$\large \text{Total length} =   \sum \limits_{n=1}^7 a_n$$

ganeshie8 · Answer

plugin the expression for nth term, $a_n$ above ^^

anonymous · Answer

ok thnx

ganeshie8 · Answer

$$\large \text{Total length} =   \sum \limits_{n=1}^7 6+(n-1)*3$$

ganeshie8 · Answer

simplifying gives you :

$$\large \text{Total length} =   \sum \limits_{n=1}^7 (3n+3)$$