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.

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