Task Sets: Derive geometric series formula - Common Core Math - HS Algebra

1.

Find the sum of the geometric series $3 + 6 + 12 + 24 + 48 + 96$ .

Use the formula $S = \dfrac{a(r^n - 1)}{r - 1}$ .

2.

Find the sum of the geometric series $80 + 40 + 20 + 10 + 5$ .

Use the formula $S = \dfrac{a(1 - r^n)}{1 - r}$ .

3.

Find the sum of the geometric series $1 + 3 + 9 + 27 + 81 + 243$ .

Use the formula $S = \dfrac{a(r^n - 1)}{r - 1}$ .

4.

What is the sum of the geometric series $7 + 7 + 7 + 7 + 7 + 7$ (six terms)?

A.

$\dfrac{7(1 - 1^6)}{1 - 1} = \dfrac{0}{0}$ , which is undefined.

B.

$7^6 = 117649$

C.

$S = na = 6 \times 7 = 42$

D.

$S = 7 \times 6^1 = 42$ using the formula.

5.

For the geometric series with $a = 4$ , $r = \frac{1}{2}$ , $n = 8$ , which formula form is most convenient to use?

A.

$S = \dfrac{a(r^n - 1)}{r - 1}$ , since $r < 1$ .

B.

$S = \dfrac{a(1 - r^n)}{1 - r}$ , since $r < 1$ .

C.

$S = na$ , since $r = 1$ .

D.

Either form gives the same result, and both are equally convenient.

Exercises: Geometric Series Formula