Answer:
d=$15,
Explicit formula: [tex]a_n=120+(n-1)15[/tex]
[tex]a_{12}=285[/tex]
At 27 month Ginni make a deposit at least $500.
Step-by-step 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
[tex]a_3=a+(3-1)15[/tex]
⇒ [tex]150=a+30\thinspace gives\thinspace a=120[/tex]
Explicit formula for arithmetic sequence is
[tex]a_n=a+(n-1)d[/tex]
⇒ [tex]a_n=120+(n-1)15[/tex]
Now, we have to find the amount of Ginni in 12th deposit i.e n=12
[tex]a_{12}=120+(12-1)15[/tex]
⇒ [tex]a_{12}=120+165=285[/tex]
Now, we have to find at what month Ginni make a deposit at least $500.
[tex]a_n=120+(n-1)15[/tex]
⇒ [tex]500=120+(n-1)15[/tex]
⇒ [tex]n-1=\frac{380}{15}[/tex]
⇒ [tex]n=26.33\sim27[/tex]
hence, at 27 month Ginni make a deposit at least $500.
