Question

Consider the geometric sequence who’s first few entries are two, 10, 15, 250, 1250, 6250,… Let y be the entry in position X. Find an equation expressing y in terms of X, and explain in detail why your equation is valid.

Answer 1

According to the given data we have the following geometric sequence:

two, 10, 15, 250, 1250, 6250

two, 10, 15, 250, 1250, 6250 are a geometric sequence so, put ai the entry in position 1 so ai=2=2*5^1-1

a2 would be the entry in position 2 so a2=10=5^2-1*2

y would be the entry in position x so an equation expressing y in terms of X would be the following:

equation expressing y in terms of X is y=2x5^x-1

`y=2x5\wedge x\text{ -1}`