Geometric sequence question in IB HL mathematics paper 1 november 2010

[bajoriay]

Homework Statement

The sum S n of the first n terms of a geometric sequence whose nth term is u n is given by

7ⁿ-aⁿ / 7ⁿ

Where a > 0

Find an expression for u_n

Find the first term and the common ratio of the sequence

Consider the sum to infinity of the sequence

Determine the values of a such that the sum to infinity exists
Find the sum to infinity when it exists

I tried to make it equal to the equation for S_n but it doesn't seem to be helping.

Thanks in advance

 

[Ray Vickson]

Homework Statement

The sum S n of the first n terms of a geometric sequence whose nth term is u n is given by

7ⁿ-aⁿ / 7ⁿ

Where a > 0

Find an expression for u_n

Find the first term and the common ratio of the sequence

Consider the sum to infinity of the sequence

Determine the values of a such that the sum to infinity exists
Find the sum to infinity when it exists

I tried to make it equal to the equation for S_n but it doesn't seem to be helping.

Thanks in advance

Do you mean
$$u_n = \frac{7^n - a^n}{7^n},$$
of do you mean
$$u_n = 7^n - \frac{a^n}{7^n}?$$
Use parentheses, like this: (7^n - a^n)/7^n or 7^n - (a^n/7^n).

 

[haruspex]

I tried to make it equal to the equation for S_n but it doesn't seem to be helping.

That's the right way. Pls post your working.