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.

Answer 1

1. 15 dollars
2. Deposit=15*month+105
3. Deposit=15*12+105=$285
4.
500=15*month+105
395=15*month
26.33=month
Round up to 27 for the nearest whole month, so month 27.

Hope this helps!

Answer 2

d=$15,

Explicit formula:
`a_n=120+(n-1)15`

`a_(12)=285`

At 27 month Ginni make a deposit at least $500.

Explanation:

Given that 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.

we have to find the common difference i.e d

-- , -- , $150, x, $180 , -------

Let $x be the 4th deposit.

∴ x-150=180-x ⇒ 2x=330 ⇒ x=165

Common difference,d=165-150=$15

Let us find the first tem i.e the value of a

`a_3=a+(3-1)15`

⇒
`150=a+30\thinspace gives\thinspace a=120`

Explicit formula for arithmetic sequence is

`a_n=a+(n-1)d`

⇒
`a_n=120+(n-1)15`

Now, we have to find the amount of Ginni in 12th deposit i.e n=12

`a_(12)=120+(12-1)15`

⇒
`a_(12)=120+165=285`

Now, we have to find at what month Ginni make a deposit at least $500.

`a_n=120+(n-1)15`

⇒
`500=120+(n-1)15`

⇒
`n-1=(380)/(15)`

⇒
`n=26.33\sim27`

hence, at 27 month Ginni make a deposit at least $500.