Find a1 if sn=-26,240 r=-3 n=8?

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Presuming this is a geometric sequence and you have the sum of the first 8 terms and you know the common ratio and need to find the first term, then we use this equation:

Sn = a1(1 - r^n) / (1 - r)

We have Sn, r, and n, so substitute what we know and solve for a1 (which I'll change to just a to make things easier to read:

-26240 = a(1 - (-3)^8) / (1 - (-3))
-26240 = a(1 - 6561) / (1 + 3)
-26240 = a(-6560) / 4
-26240 = -1640a

a = 26240 / 1640
a = 16

The first term is 16.

Hope this helped. Please give best answer if it did....Show more

s8 = a1(1-r^8)/(1-r)
-26240 = a1 (1-(-3)^8) /(1-(-3))
-26240 = a1 (1-(6561)) /4
-26240 = a1 (-6560/4)
-26240 = a1 * (-1640)
a1 = 26240/1640
a1 = 16...Show more

S8 = a r ^7________assuming a geometric progression
26420 = (-3)^7 a
a = - 26420 / 3^7
a = - 12 . 1...Show more

sn = a1*(r^n -1)/(r -1)
Substitute the given values and solve for a1.
-26240 = a1*((-3)^8 -1)/(-3 -1)
.. = a1*(6560/-4)
.. = -1640*a1
-26240/-1640 = a1 = 16...Show more

　
Geometric sum: Sn = a (r^n−1) / (r−1)

S₈ = −26240, r = −3
a ((−3)^8−1) / (−3−1) = −26240
a (6561−1) / −4 = −26240
a (6560)/−4 = −26240
−1640a = −26240
a = 16

Matthew, just read your comment to llaffer
The reason Google calculator gave you the wrong answer is probably because you entered it incorrectly.
(−3)^8 = 6561 ----> Correct
−3^8 = −(3^8) = −6561 ----> Incorrect
https://www.google.ca/search?source=hp&ei=mntlWszBK87AtQW_t6bQDg&q=%28-3%29%5E8&oq=%28-3%29%5E8&gs_l=psy-ab.3..38l5j0i30k1l5.1349.11512.0.11923.15.10.4.0.0.0.658.1600.4j5j5-1.10.0....0...1.1.64.psy-ab..1.14.1638.0..0.0.Ayj6dNXiFb0

Remember: any real number (whether positive or negative) raised to an even power will be positive....Show more