SOLUTION
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.
Since it follows an arithmetic sequence, T n = a + ( n- 1 ) d
Month 3 , T 3 = a+ ( 3 - 1 ) d = 150
a + 2 d = 150 --------------------- equ 1
Month 5 , T 5 = a + ( 5 - 1 ) d = 180
a + 4 d = 180 ...........................equ 2
Solving the two equations, we have :
a - a + 4 d - 2 d = 180 - 150
2 d = 30
Divide both sides by 2 , we have:
d = 15
Let us put d = 15 in equ 1 , we have a + 2 d = 150
a + 2 ( 15 ) = 150
a + 30 = 150
a = 150 - 30
a = 120
From the solution,
Month 1 = 120
Month 2 = 120 + 15 = 135
Month 3 = 135 + 15 = 150
Month 4 = 150 + 15 = 165
Month 5 = 165 + 15 = 180
1. What is the common difference for the deposits made each month? d = 15
2. Write an explicit formula for this arithmetic sequence.
Recall that Tn = a + ( n - 1 ) d
Tn = 120 + ( n - 1 ) 15
Tn = 120 + 15 n - 15
Tn = 120 - 15 + 5n
Tn = 105 + 15n
3. What is the amount of Ginny's deposit in the 12th month?
Tn = 105 + 15n
T 12 = 105 + 15 ( 12 )
T 12 = 105 + 180 = 285
4. At what month will Ginny first make a deposit that is at least $500?
Using Tn = 105 + 15 n = 500
105 + 15 n = 500
15 n = 500 - 105
15 n = 395
Divide both sides by 15 , we have :
n = 26 . 33
n = 27