Question

The first term of a geometric series is 14 and the 6ᵗʰ term is 448 . 2.1.1 Calculate the value of the constant ratio, r

Answer 1

Explanation:

a geometric series means that

sn = sn-1 × r

with r being a constant for the whole series.

so,

s1 bring the starting value, we get

s2 = s1 × r

s3 = s2 × r = s1 × r × r

s4 = s3 × r = s2 × r × r = s1 × r × r × r

we see,

sn = s1 × r^(n-1)

in our case

s1 = 14

n = 6 and n-1 = 5 :

s6 = 448 = 14 × r⁵

r⁵ = 448/14 = 32 = 2⁵

therefore,

r = 2