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. if you were to write this series in summation notation, give i. the lower limit of the sum ii. the upper limit of the sum iii. the explicit formula of the sum b. find the total number of beads in the necklace. explain your method for finding the total number of beads. show all your work.

a)

i.the lower limit of the sum

: n=1

ii.the upper limit of the sum

: n=18

iii.the explicit formula of the sum

:

b)  1,125 beads

Step-by-step explanation:

a) The number of beads per row of Dante's necklace is given by the series:

3 + 10 + 17 + 24 + ...

The first term of this series is .

There is a constant difference of .

To write this series in summation notation, we need to determine the explicit formula which is given by:

We plug in the values to get:

The summation notation is given by:

b) The total number of beads in the necklace is given by the sum of the first 18 terms of the sequence.

This is given by

We substitute the values to obtain:

Therefore the total number of beads is 1125

-14

step-by-step explanation:

2x2 – 2(x+4)

=2x2-2（5+4）

=4-2×9

=4-18

=-14

3 is greater then both of those numbers