Graph the six terms of a finite series where a₁ = -3 and r = 1.5

Solution:

Given, the series is in geometric progression

First term, a₁ = -3

Common ratio, r = 1.5

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

Geometric progression can be represented by the formula,

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

\(a_{2}= -3(1.5)^{2-1}\\a_{2}=-3(1.5)^{1}\\a_{2}=-4.5\)

\(a_{3}= -3(1.5)^{3-1}\\a_{3}=-3(1.5)^{2}\\a_{3}=-6.75\)

\(a_{4}= -3(1.5)^{4-1}\\a_{4}=-3(1.5)^{3}\\a_{4}=-10.125\)

\(a_{5}= -3(1.5)^{5-1}\\a_{5}=-3(1.5)^{4}\\a_{5}=-15.188\)

\(a_{6}= -3(1.5)^{6-1}\\a_{6}=-3(1.5)^{5}\\a_{6}=-22.781\)

Therefore, the graph of the six terms of a finite series are mentioned above.

Graph the six terms of a finite series where a₁ = -3 and r = 1.5

Summary:

The graph of the six terms of a finite series where a1 = -3 and r = 1.5 is mentioned above.