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shainaanderson24
22.11.2019 •
Mathematics
What is the first term in a geometric sequence if the common ratio is −3 and the sum of the first six terms is 1,274? hint: cap s sub n equals start fraction a sub one (one minus r to the power of n end power )over one minus r end fraction comma r ≠ 1, where a1 is the first term and r is the common ratio.
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Ответ:
Answer is -7
Work Shown:
s_n = a_1*(1-r^n)/(1-r)
s_6 = a_1*(1-r^6)/(1-r)
s_6 = x*(1-(-3)^6)/(1-(-3))
s_6 = x*(1-729)/(1+3)
s_6 = x*(-728)/4
s_6 = x*(-182)
s_6 = -182x
-182x = s_6
-182x = 1274
x = 1274/(-182)
x = -7 is the first term of the geometric sequence
Extra info:
The first six terms of this geometric sequence is
-7, 21, -63, 189, -567, 1701
those six terms add to
-7+21+(-63)+189+(-567)+1701 = 1274
which verifies we have the right answer.
Ответ:
b i think
im kinda dum lol
Step-by-step explanation: