Final answer:
To find the sum of the first 10 terms of a geometric series, use the given terms to find the common ratio and the first term, then use the formula for the sum of a geometric series. After calculation, the sum comes up to 349525.
Step-by-step explanation:
To find the sum of the first 10 terms of a geometric series, we need to find the common ratio and the first term. Let's denote the first term as a and the common ratio as r. We are given that the second term is -43 and the fifth term is 3281.
We can use the formula for the nth term of a geometric series to set up two equations:
a * r = -43 (equation 1)
a * r^4 = 3281 (equation 2)
By dividing equation 2 by equation 1, we can solve for r:
r^3 = -3281/-43
r^3 = 76
r = 4
Now, we can substitute the value of r into equation 1 to find the first term:
a * 4 = -43
a = -43/4
Finally, we can use the formula for the sum of the first n terms of a geometric series:
Sum = a * (1 - r^n) / (1 - r)
Plugging in the values given, we get:
Sum = (-43/4) * (1 - 4^10) / (1 - 4)
Sum = -43 * (1 - 1048576) / -3
Sum = 349525