Starting from 1993 john saved 5 dollars in that year for the subsequent years, he saved 3 times the saved amount of the preivous year. what is Johns total savings at the end of 1998?
looks like a geometric sequence with
a=5
r=3
n=5
You should know the formula if you are studying the topic.
im not studying this topic.... so i don't know
No problem! I can help you with that. To find John's total savings at the end of 1998, we need to calculate the sum of the geometric sequence.
In a geometric sequence, each term is found by multiplying the previous term by a constant called the common ratio (r in this case).
The formula to find the sum of a geometric sequence is:
Sn = a * (1 - r^n) / (1 - r)
Where:
- Sn is the sum of the sequence
- a is the first term
- r is the common ratio
- n is the number of terms
In this case, the first term (a) is $5, the common ratio (r) is 3 (as each subsequent year's savings is 3 times the previous year's savings), and the number of terms (n) is 5 (since we need to find the total savings at the end of 1998).
Plugging the values into the formula:
Sn = 5 * (1 - 3^5) / (1 - 3)
Calculating this gives us:
Sn = 5 * (1 - 243) / -2
Simplifying further:
Sn = 5 * (-242) / -2
Sn = 5 * 121
Sn = $605
Therefore, John's total savings at the end of 1998 would be $605.