University:
Davenport University
Course:
MATH 120 | College Mathematics
Academic year:

2022
Views:

162

Pages:

3
Author:

tubofib

Arithmetic and Geometric Series – Worksheet General formula for an arithmetic series: General formula for a geometric series: 1) Find the designated sum of the arithmetic series a) 𝑆14 of 3+7+11+15+⋯ b) 𝑆11 of −13−11−9−7−⋯ c) 𝑆9 of 22+20+18+16+⋯ d) 𝑆35 of −2−5−8−11−⋯ 2) Determine the sum of each arithmetic series a) 6+13+20+⋯+69 c) 5−8−21−⋯−190 b) 4+15+26+⋯+213 d) 100+90+80+⋯−100 3) Find the designated sum of the geometric series a) 𝑆7 of 4+8+16+32+⋯ b) 𝑆13 of 1−6+36−216+⋯ c) 𝑆17 of 486+162+54+18+⋯ d) 𝑆6 of 3+15+75+375+⋯ 4) Determine 𝑆𝑛 for each geometric series a) 𝑎=6, 𝑟=2, 𝑛=9 b) 𝑓 1 =2, 𝑟=−2, 𝑛=12 c) 𝑓 1 =729, 𝑟=−3, 𝑛=15 d) 𝑓 1 =2700, 𝑟=10, 𝑛=8 5) If the first term of an arithmetic series is 2, the last term is 20, and the increase constant is +2 … a) Determine the number of terms in the series b) Determine the sum of all the terms in the series 6) A geometric series has a sum of 1365. Each term increases by a factor of 4. If there are 6 terms, find the value of the first term. Answers 1) a) 406 b) -33 c) 126 d) -1855 2) a) 375 b) 2170 3) a) 508 b) 1 4) a) 3066 b) -2730 c) -1480 729 d) 11 865 c) 813 718 431 c) 2 615 088 483 d) 2.999 999 97 × 10! " 5) a) 𝑛 = 10 b) 𝑆! " = 110 6) 𝑡! = 1 d) 0