In January, you start a holiday savings account with a deposit of $20. You decide to increase each monthly deposit by five dollars until the end of the year. Ho

Question

In January, you start a holiday savings account with a deposit of $20. You decide to increase each monthly deposit by five dollars until the end of the year. How much money will you have saved by the end of the year?

Answer 1

Jane is on the right track.

 

To find our last deposit, we use the formula...

 

a_n = a₁ + (n - 1)d

a_n = 20 + (12 - 1)5 = 20 + 55 = 75

 

To find the total money you'll have...

 

S_n = n(a₁ + a_n)/2 = 12(20 + 75)/2 = 6(95) = 570

 

In December, you'll have $570 in your account.

Answer 2

   

This problem is an arithmetic sequence problem. The formula for arithmetic sequence is

 

                        a_n = a₁ + (n – 1)d   

 

                            = $20 + (12 - 1)5

 

                            = 20 + (19)5

                            = 20 + 95

 

                         a₁₂   = $115

 

So now, you need to find the sum of 20 + 25 + 30 + .... + 115.

 

S_n = n (a₁ + a_n)/2

 

     = 12 (20 + 115)/2

 

     = 6 (20 + 115)

 

     = 6 (135)

 

     = $810