Answer:
a. The common ratio is 0.5
b) The value of the first term is 29
c) The sum of the first 5 terms is 56.1875
Step-by-step explanation:
The nth term of the geometric sequence is a
= a
, where
The sum of the nth term is S
= 
∵ The second term of a geometric sequence is 14.5
∴ n = 2
∴ a
= 14.5
∵ a
= ar
→ Equate the right sides of a
by 14.5
∵ ar = 14.5 ⇒ (1)
∵ The fifth term is 1.8125
∴ n = 5
∴ a
= 1.8125
∵ a
= a
→ Equate the right sides of a
by 14.5
∵ a
= 1.8125 ⇒ (2)
→ Divide equation (2) by equation (1)
∵
= 
∴ r³ = 0.125
→ Take ∛ for both sides
∴ r = 0.5
a. The common ratio is 0.5
→ Substitute the value of r in equation (1) to find a
∵ a(0.5) = 14.5
∴ 0.5a = 14.5
→ Divide both sides by 0.5
∴ a = 29
b) The value of the first term is 29
∵ n = 5
∴ S
= ![\frac{29[1-[0.5]^{5})}{1-0.5}](https://tex.z-dn.net/?f=%5Cfrac%7B29%5B1-%5B0.5%5D%5E%7B5%7D%29%7D%7B1-0.5%7D)
∴ S
= 56.1875
c) The sum of the first 5 terms is 56.1875