What is #s_n# of the geometric series with #a_1=4#, #a_n=256#, and #n=4#?

Answer 1

The sum is #340#.

Since the #nth# term is given as #256# but #n# is given as #4#, that means #256# is the #4th# term. But the #4th# term of a GP equals #ar^3#, where a is the first term and #r# is the common ratio of the GP. Dividing #256# by the first term (which is given as #4#) shows us that #r^3 = 256/4 = 64#.

If #r^3 = 64#, then the common ratio #r# must equal #4# as well. This gives us all the information we need to use the formula for the sum of a GP, #S = (a(r^n - 1))/(r - 1)#.

In this case, #S = (4(4^4 - 1))/(4 - 1) = (4(256 - 1))/3 = 1020/3 = 340#.

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Answer 2

Cameron Alexander

The ( s_n ) of the geometric series with ( a_1 = 4 ), ( a_n = 256 ), and ( n = 4 ) is ( s_4 = 340 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.