Sequences and Series Math Question

Question

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.

Answer 1

if r = row, then the sum of the bead in each row will be (3 + 7(r-1)), where r = 1,2,3,.....18

Then Sum = S₁¹⁸{3 + 7(r-1)} = 3+10+17+24+........+122

Not sure what the upper & lower limits mean but 3 is the max & 122 is the minimum??

Total of the beads is 18*3 + 7*Sum(1+2+3+4+.....+17) = 54+7*((18*17)/2) = 21+1071 = 1125