<u>Answer:</u>
Both accounts of Nick and Allie will have same amount of $864 in time period of 4 weeks.
<u>Solution: </u>
Given, Yesterday two friends went into a bank to open savings accounts.
Allie started by putting $783 in her account, and she will deposit an additional $27 each week.
Nick made no initial deposit, but he will add $288 more each week.
In a few weeks, the friends will have the same account balance.
Here, account balance of Allie for every week forms an A.P as
783, 810, 837, ……. With common difference 27
And, account balance of nick for every week will be
0, 288, 576, …….. with common difference 288
Let, after n weeks the balance in both accounts be equal.
Then, nth term of both series will be equal, we know that, nth term tn of A.P is a + (n – 1)d
Where, a is first term, d is common difference and n is number of terms.
Now, nth term of allie series = nth term of nick series.
783 + (n – 1) x 27 = 0 + (n – 1) x 288
Here, we used same n for both sides because n represents number of weeks and it is common to both
783 + 27n – 27 = 288n – 288
756 + 288 = 288n – 27n
261n = 1044
n = 4.
So, it will take 4 weeks to have same balance and now, substitute n value in nth term of nick series.
Hence, both accounts will have same amount of $864 in time period of 4 weeks