Question

Betsy is saying for a bird cage. She saves $1 the first week, $3 the second week, $9 the third week, and so on. All together how much money will she have saved in 5 weeks?

Answer 1

Betsy will save $121 in 5 weeks.

Explanation:

We can see that Betsy's savings are 3 times the saving of her last week. We can see that this is an geometric sequence as 1,3,9,..

To find the sum of our geometric sequence we will use
`S_(n)=a\cdot (1-r^(n))/(1-r)`, where n is number of terms we are taking sum of, a is first term of sequence and r is common ratio of the sequence.

`S_(5)=1\cdot (1-3^(5))/(1-3)`

`S_(5)=(1-243)/(-2)`

`S_(n)=(-242)/(-2)=121`

Therefore, Betsy will save $121 in 5 weeks.