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, givei.the lower limit of the sumii.the upper limit of the sumiii.the explicit formula of the sumb. Find the total number of beads in the necklace. Explain your method for finding the total number of beads.Show all your work.

Answer:a)i.the lower limit of the sum: n=1ii.the upper limit of the sum: n=18iii.the explicit formula of the sum: [tex]a_n=7n-4[/tex]b)  1,125 beadsStep-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 [tex]a_1=3[/tex].There is a constant difference of [tex]d=10-3=7[/tex].To write this series in summation notation, we need to determine the explicit formula which is given by:[tex]a_n=a_1+d(n-1)[/tex]We plug in the values to get:[tex]a_n=3+7(n-1)[/tex][tex]\implies a_n=3+7n-7[/tex][tex]\implies a_n=7n-4[/tex]The summation notation is given by:[tex]\sum^{18}_{n=1}(7n-4)[/tex]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 [tex]S_n=\frac{n}{2}(2a_1+d(n-1))[/tex]We substitute the values to obtain:[tex]S_{18}=\frac{18}{2}(2\cdot3+7(18-1))[/tex][tex]S_{18}=9(6+119)[/tex][tex]S_{18}=9(125)[/tex][tex]S_{18}=1125[/tex]Therefore the total number of beads is 1125