Question

Mike started a savings account by depositing $9. Each month he deposits more money than the month before. At the end of 41 months, he has saved $9,389.00. How much more does he deposit each month

Answer 1

$11.00 or 11

same thing :)

*plug all other answer choices inside formula as d to check your answer*

Explanation:

we need to use the arithmetic sequence formula

`S_n=(n)/(2) [2a_1+(n-1)d]\\`

`a_1=9\\n=41\\d=11 \\\\S_4_1=(41)/(2)[ (2)(4)+(41-1)(11)] \\\\S_4_1=(41)/(2) [8+(40)(11)]\\\\\S_4_1=(41)/(2) (18+440)\\\\S_4_1=(41)/(2) (458)\\\\S_4_1=20.5 (458)\\\\S_4_1=9,389`

He deposit 11 each month is right because the sum of the series (
`S_n`) is 9,389 and he saved 9,389 at the end of the 41 months.

Answer 2

We have to calculate how much more money does Mike deposit each month. This can be done using the formula for the arythmetic sequence; S n = n/2 * ( a1 + an ). Here: a 1 = 9, n = 41 and a n = a 1 + ( n-1 ) d = 9 + 40 d. So : 9,389 = 41/2 * ( 9 + 9 + 40 d ); 9,389 = 41 / 2 * ( 18 + 40 d ); 9,389 = 41 * ( 9 + 20 d ) ; 9,389 = 369 + 820 d; 820 d = 9,389 - 369; 820 d = 9,020; d = 9,020 : 820; d = 11. Answer: He deposits $11 more each month.