The seventh term, u7 , of a geometric sequence is 108. the eighth term, u8 , of the sequence is 36 . (a) write down the common ratio of the sequence. [1 mark] (b) find u1 . [2 marks] the sum of the first k terms in the sequence is 118 096 . (c) find the value of k . [

To solve the first part we are going to use the formula for the nth therm of geometric sequence: 
where 
is the nth term
is the first term
is the ratio 
is the position of the term in the sequence

a. The ratio of a geometric sequence is . We know for our problem that and . Lets replace those values in our formula to find :



We can conclude that the ratio of our geometric sequence is .

b. To find  we are going to use the formula for the nth therm of geometric sequence, the ratio, and the given fact that :







We can conclude that the first therm, , of our geometric sequence is 78732.

c. To solve this one we are going to use the formula for the sum of the first nth terms of a geometric sequence: 
where
is the sum of the first  terms
is the first term 
is the common ratio 
is the number of terms 

We know for our problem that , and we also know for previous calculations that  and . So lets replace those values in our formula to find :





We can conclude the the sum of the first 10 terms of our geometric sequence is 118096.