20 The second term of a geometric sequence is 14.5 and the fifth term is 1.8125
a Determine the common ratio,
b Find the value of the first term.
€ Find the sum of the first 5 terms,

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 =

∴ S = 56.1875

c) The sum of the first 5 terms is 56.1875