Question

Help!! So confused!
Dante is making a necklace with 18 rows of tiny beads in which the number of beads per row is given by the series 3 + 10 + 17 + 24 + ...

a. Use summation notation to write the series. Explain what the numbers in the summation notation represent in this situation and how you found the expression used in the summation.

b. Find the total number of beads in the necklace. Explain your method for finding the total number of beads.

Answer 1

find the difference between the successive terms...

Answer 2

notice a trend there?

Answer 3

They each go up by 7

Answer 4

what is such a series called?

Answer 5

arithmetic

Answer 6

good job.. so you got the answer for (a) now?

Answer 7

How would I write the summation notation for question a?

Answer 8

ok, start by writing what we have..
3 = 3 + 0*7
10 = 3 + 1*7
17 = 3 + 2*7
and so on
18 times
a_n = a_0 + (n-1)*d
that give you the n'th number

Answer 9

ok

Answer 10

now, all you gotta do is add em up
\[
S = \sum_{n=1}^{18}a_n\\
S=\sum_{n=1}^{18}a_0+(n-1)d
\]

Answer 11

where a0=?
d=?

Answer 12

d= the common difference so d would = 7

Answer 13

and a would be the 1st term so would that = 3?

Answer 14

yep

Answer 15

yay! Okay so to find the total number of beads which is question #b I would multiply?

Answer 16

no.. total mean a sum...
3 apples in one hand and 4 apples in the other.. total is? (add)

Answer 17

so, the sum of arithmatic series to nth term is:
\[S_n={n\over2}[2a_0+(n-1)d]\]

Answer 18

how many rows you have? 18..
so, n = 18
and rest you already have

Answer 19

ohh ok. so would the answer be 1125 beads?

Answer 20

i gues.. (9)(6+17*7)