The sum of the first k terms in the sequence is 118096, find the value of k. The first term is 78732 the common ratio is 1/3.

Mathematics

1 answer:

FrozenT [24]2 years ago

8 0

Answer:

k = 10

Step-by-step explanation:

The sum of k terms of a geometric sequence with first term a1 and common ratio r is given by ...

... Sk = a1·(1 -r^k)/(1 -r)

For the given numbers, this is ...

... 118096 = 78732·(1 -(1/3)^k)/(1 -1/3)

Manipulating this to get the term containing k, we have

... 1 -(2/3)(118096/78732) = (1/3)^k

... 1/59049 = (1/3)^k

Taking logarithms, we get

... -log(59049) = -k·log(3)

... log(59049)/log(3) = k = 10

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