Final answer:
To find a1 in a geometric series, you can use the formula S_n = a_1(1 - r^n)/(1 - r), where S_n is the sum of the series, a_1 is the first term, r is the common ratio, and n is the number of terms. Given the values S_8 = 765, n = 8, and r = 2, the first term a_1 is -3.
Step-by-step explanation:
To find a1 in a geometric series, we can use the formula:
S_n = a_1(1 - r^n)/(1 - r)
where S_n is the sum of the series, a_1 is the first term, r is the common ratio, and n is the number of terms.
Given that S_8 = 765, n = 8, and r = 2, we can plug these values into the formula to find a_1:
765 = a_1(1 - 2^8)/(1 - 2)
765 = a_1(1 - 256)/(-1)
765 = a_1(-255)
To solve for a_1, we can divide both sides of the equation by -255:
a_1 = 765/-255
a_1 = -3