Answer:
* The value of a1 = 945.65 ⇒ answer c
Step-by-step explanation:
* Lets revise the geometric series
- There is a constant ratio between each two consecutive numbers
- Ex:
# 5 , 10 , 20 , 40 , 80 , ………………………. (×2)
# 5000 , 1000 , 200 , 40 , …………………………(÷5)
* General term (nth term) of a Geometric Progression:
- U1 = a , U2 = ar , U3 = ar² , U4 = ar³ , U5 = ar^4
- Un = ar^n-1, where a is the first term , r is the constant ratio
between each two consecutive terms, n is the position
of the term
- The sum of first n terms of a Geometric series is calculate
from Sn = [a1 (1 - r^n)]/(1 - r) , where a1 is the first term, r is the
common ratio and n is the number of the terms
* Lets solve the problem
∵ Sn = 88,560
∵ r = 2.2
∵ n = 6
∵ Sn = [a1 (1 - r^n)]/(1 - r)
∴ 88,560 = [a1 (1 - 2.2^6)]/(1 - 2.2) ⇒ simplify up and down
∴ 88,560 = [a1 (-112.379904)]/(-1.2) ⇒ simplify the fraction
∴ 88,560 = a1 (93.64992) ⇒ divide both sides by 93.64992
∴ a1 = 945.6494998 ≅ 945.65
* The value of a1 = 945.65
