Laverne starts counting out loud by 5's. She starts with 7. As Laverne counts, Shirley sums the numbers Laverne says. When the sum finally exceeds 5000, Shirley runs screaming from the room. What number did Laverne last say before Shirley flees?
Just use your formula for an arithmetic sequence
n/2 (2*7+(n-1)*5 > 5000
n > 44
So, the 44th term is 7+43*5 = 222
check:
43/2 (14+42*5) = 4816
4816+222 = 5038
5 goes evenly into 5000, but there is an extra 2 in there...
not sure where Steve is going
counting by 5's, the largest 1st number OVER 5000 in one counting step would be 5005
we want the *sum* to exceed 5000 ...
To find the number that Laverne last says before Shirley flees, we need to determine how Laverne counts by 5s and calculate the sum of the numbers she says until the sum exceeds 5000.
Laverne starts counting by 5s, beginning with 7. So, she would say 7, 12, 17, 22, and so on. The pattern is adding 5 to the previous number each time.
To calculate the sum of the numbers she says, we can create a table:
| Number | Sum So Far |
|--------|------------|
| 7 | 7 |
| 12 | 19 |
| 17 | 36 |
| 22 | 58 |
| ... | ... |
Starting with 7, we add 5 each time to the previous number and keep track of the sum. Continuing this process, we find the following sums:
7, 19, 36, 58, 83, 113, 148, 188, 233, 283, 338, 398, 463, 533, 608, 688, 773, 863, 958, 1058, 1163, 1273, 1388, 1508, 1633, 1763, 1898, 2038, 2183, 2333, 2488, 2648, 2813, 2983, 3158, 3338, 3523, 3713, 3908, 4108, 4313, 4523, 4738, 4958
By calculating the sum of the numbers up to this point, we can see that the sum exceeds 5000 after the number 4958. Therefore, the number that Laverne last says before Shirley flees is 4958.