Question

How many terms are in this series: 1 – 2 + 4 – 8 + . . . – 131072

Answer 1

-0

Answer 2

this is a geomeric series

Answer 3

geometric*

Answer 4

if you divide two consecutive terms, you get a ratio of -2

Answer 5

$$\Large (-2)^0 + (-2)^1 + (-2)^2 + (-2)^3+ ... (-2)^{n-1} $$

Answer 6

an=a1(r)^n-1

Answer 7

so you need to solve

(-2)^(n-1) = – 131072

Answer 8

you can also solve this using logarithms

Answer 9

n=18

Answer 10

Determine the sum: 25 + 5 + 1 + ...

Answer 11

the ratio is 1/5

Answer 12

$$\Large \sum_{n=0}^{\infty} ar^{n-1}= \frac{a}{1-r}~,~ |r| < 1 $$

Answer 13

a1=25

Answer 14

right

Answer 15

25/1/5

Answer 16

be careful

Answer 17

$$\Large \sum_{n=0}^{\infty} ar^{n-1}= \frac{a}{1-r}~,~ |r| < 1
\\~\\\Large \sum_{n=0}^{\infty} 25\cdot (1/5)^{n-1}= \frac{25}{1-1/5}~,~ |1/5| < 1 ~\checkmark
\\~\\ \Large \frac{25}{4/5} = 25 \cdot \frac 5 4


$$

Answer 18

31.25!

Answer 19

i almost forgot to do 1-1/5