Question #4af87

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Answer 1 · 2016-09-18T15:02:43

The sum is #2,548#.

We have to start by finding the number of terms. This can be found by solving for #n# in the formula #t_n = a xx r^(n - 1)#.

#1,701 = 7 xx 3^(n - 1)#

#243 = 3^(n - 1)#

#ln(243) = ln(3^(n - 1))#

#ln243 = (n- 1)ln3#

#n - 1 = ln243/ln3#

#n - 1 = ln(3^5)/ln(3^1)#

#n - 1 = (5ln3)/(1ln3)#

#n - 1= 5#

#n = 6#

Notice that at the 2nd step we could have also just equated exponents.

We will now use the formula #s_n = (a(1 - r^n))/(1 - r)# to determine the sum of the first six terms of this series.

#s_6 = (7(1 - 3^6))/(1 - 3)#

#s_6 = (7(1 - 729))/(-2)#

#s_6 = 2,548#

Hence, the sum of the geometric series with the given information is #2,548#.

Hopefully this helps!