Graph the six terms of a finite sequence where a₁ = 5 and r = 1.25

Solution:

Given, the series is in Geometric Progression

First term, a₁ = 5

Common ratio, r = 1.25

We have to find the six terms of a finite sequence.

Geometric progression can be represented by the formula,

\(f(n) = a_{1}(r)^{n-1}\)

\(a_{2} = 5(1.25)^{2-1}\\a_{2} = 5(1.25)\\a_{2}=6.250\)

\(a_{3} = 5(1.25)^{3-1}\\a_{3} = 5(1.25)^{2}\\a_{3} = 7.813\)

\(a_{4} = 5(1.25)^{4-1}\\a_{4} = 5(1.25)^{3}\\a_{4} = 9.766\)

\(a_{5} = 5(1.25)^{5-1}\\a_{5} = 5(1.25)^{4}\\a_{5} = 12.207\)

\(a_{6} = 5(1.25)^{6-1}\\a_{6} = 5(1.25)^{5}\\a_{6} = 15.259\)

Therefore, the points on the graph will be (1,5), (2,6.25), (3,7.813), (4,9.766), (5,12.207), (6,15.259).

Graph the six terms of a finite sequence where a₁ = 5 and r = 1.25

Summary:

The six terms of a finite sequence where a₁ = 5 and r = 1.25 are 6.250, 7.813, 9.766, 12.207 and 15.259.