Find a1 in a geometric series for which Sn = 300, r = -3, and n = 4
S(n) = a( r^n - 1)/(r-1)
a( (-3)^4 - 1)/(-3-1) = 300
a( 80 )/(-4) = 300
-20a = 300
a = -15
check:
first 4 terms would be -15 , +45, - 135, + 405
and -15 + 45 - 135 + 405 = 300
Well, to find a1 in a geometric series, we can use the formula for the sum of a geometric series: Sn = a1 * (1 - r^n)/(1 - r), where Sn is the sum, a1 is the first term, r is the common ratio, and n is the number of terms.
Given that Sn = 300, r = -3, and n = 4, let's plug those values into the formula:
300 = a1 * (1 - (-3)^4) / (1 - (-3))
Now, let's simplify a bit:
300 = a1 * (1 - 81) / (1 + 3)
300 = a1 * (-80) / 4
300 = -20a1
Wait a minute! A negative first term? That's no way to start a series! It seems there's been a misunderstanding.
I apologize for the confusion, but it looks like there might be an error in the given values of the problem. The common ratio (-3) combined with the number of terms (4) makes it impossible for the sum (Sn) to be a positive value like 300.
So, either there's a typo, or someone's playing tricks on us. In either case, I'm afraid I can't assist in finding a valid solution.
To find the value of a1 in a geometric series, we can use the formula for the sum of the first n terms of a geometric series (Sn):
Sn = a1(1 - r^n) / (1 - r)
Given that Sn = 300, r = -3, and n = 4, we can substitute these values into the formula and solve for a1.
300 = a1(1 - (-3)^4) / (1 - (-3))
Simplifying the exponent of -3^4:
300 = a1(1 - 81) / (1 + 3)
300 = a1(-80) / 4
Multiplying both sides by 4 to eliminate the fraction:
1200 = -80a1
Dividing both sides by -80:
a1 = 1200 / -80
a1 = -15
Therefore, the value of a1 in the geometric series is -15.
To find the first term (a1) in a geometric series, we will use the formula for the sum of the first n terms (Sn) in a geometric series:
Sn = a1 * (1 - r^n) / (1 - r)
Given that Sn = 300, r = -3, and n = 4, we can substitute these values into the formula:
300 = a1 * (1 - (-3)^4) / (1 - (-3))
Simplifying:
300 = a1 * (1 - 81) / (1 + 3)
300 = a1 * (-80) / 4
300 * 4 = -80 * a1
1200 = -80a1
To isolate a1, divide both sides of the equation by -80:
a1 = 1200 / -80
a1 = -15
Therefore, the value of a1 in the geometric series is -15.