Question

The deposits Ginny makes at her bank each month form an arithmetic sequence. The deposit for month 3 is $150, and the deposit for month 5 is $180. Answer the questions below and show all work.

1. What is the common difference for the deposits made each month?

Somebody please show me how I can solve this? I'm pretty sure it is 15, but I need to show work somehow.

Answer 1

@JamesJ @satellite73 @campbell_st @amistre64

Answer 2

ok... so you need to find the common difference

in a 2 month period the value of the deposit increases by $30

so $30/2 is the monthly increase in the deposit or the common difference.

Answer 3

if you need an algebraic solution then

a term in an arithmetic sequence is

\[T_{n} = a + (n - 1) d\]

a = 1st term, n = number of terms and d = common difference

so

\[150 = a + (3 -1)d \]

\[180 = a + ( 5 - 1)d\]

simplifying you have

Equation 1
\[150 = a + 2d\]

equation 2
\[180 = a + 4d \]

solve simultaneously by elimination

Equation2 - Equation 2

a + 4d = 180
- a + 2d = 150
----------------
2d = 30

d = 15

Answer 4

Thanks, the formula is just what I was looking for! Could you possibly help me write and explicit formula for the sequence now? @campbell_st

Answer 5

so if you know d

then you need to find a the 1st deposit or 1st term

\[150 = a + (3 -1)15\]


a = 120

so the formula for any deposit is

\[T_{n} = 120 + (n -1)15\]

just simplify the formula above

Answer 6

So \[a _{n}=15n+105\] ?

Answer 7

thats about it... well done..

Answer 8

Thanks a ton!