Dante is making a necklace with 18 rows of tiny beads in which the

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, 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.

1 Answer

  • a.i. Lower limit = 0

    a.ii. Upper limit = 17

    a.iii. Explicit formula of the sum

    ₁₇

    Σ (3+7i)

    ͥ ⁼⁰

    b. Total number of beads =

    (3+7•0)+ (3+7•1)+ (3+7•2)+ (3+7•3)+ (3+7•4)+ (3+7•5)+ (3+7•6)+ (3+7•7)+ (3+7•8)+ (3+7•9)+ (3+7•10)+ (3+7•11)+ (3+7•12)+ (3+7•13)+ (3+7•14)+ (3+7•15)+ (3+7•16)+ (3+7•17) =

    (3+0)+ (3+7)+ (3+14)+ (3+21)+ (3+28)+ (3+35)+ (3+42)+ (3+49)+ (3+56)+ (3+63)+ (3+70)+ (3+77)+ (3+84)+ (3+91)+ (3+98)+ (3+105)+ (3+112)+ (3+119) =

    (3)+ (10)+ (17)+ (24)+ (31)+ (38)+ (45)+ (52)+ (59)+ (66)+ (73)+ (80)+ (87)+ (94)+ (101)+ (108)+ (115)+ (122) =

    1125....................ANS

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