Chapter exploration

Sequences and series

Explore

Use the worked example below, then change one input or assumption. Predict which part of the answer must change before calculating.

Explore this related example, then return to the prediction task above.

Drag the slider to change n and compare the plotted values.

Indexn = 5

term uₙ at n = 5

0.0032

sum Sₙ at n = 5

0.2062

Key idea

With ratio $r=0.4$ the terms shrink geometrically and the partial sums level off at $S_\infty=\frac{a}{1-r}$ .

Ideas to try

Slide to a large

n

: the running total settles at

S_\infty=\frac{0.4}{12(0.8)(0.2)}\approx0.208