Question 1198920
<br>
The amounts put in the piggy bank in each month form an arithmetic sequence with a common difference of 1.75.<br>
The sum of the terms of an arithmetic sequence is<br>
(number of terms) times (average of the terms)
= (number of terms) times (average of first and last terms)
= (number of terms) times ((first plus last)/2)
= (half the number of terms) times (first plus last)<br>
The sum of the 12 terms for the 12 months is the final amount, 157.50, so<br>
6(first plus last) = 157.50
first plus last = 157.50/6 = 26.25<br>
The sum of the 6th and 7th terms is the same as the sum of the first and last; and the difference between the 6th and 7th terms is 1.75.  Let x and y be the amounts put in the piggy bank in the 6th and 7th months; then<br>
y+x=26.25
y-x=1.75
2y=28
y=14<br>
The amount put in the piggy bank in the 7th month (July) was $14.<br>
The amount put in the piggy bank in the first month was $14, minus the common difference of $1.75 6 times: $14-6($1.75) = $14-$10.50 = $3.50.<br>
The amounts put in the piggy bank in each month were then<br>
$3.50, $5.25, $7, $8.75, $10.50, $12.25, $14, $15.75, $17.50, $19.25, $21, and $22.75<br>
The amount in the piggy bank after April's deposit was<br>
ANSWER: $3.50 + $5.25 + $7 + $8.75 = $24.50<br>