Please help

Question

what is the seventh term of the geometric sequence given by the explicit rule an a_n=5(5)^n-1

Answer 1

a_n = 5(5)^(n-1)

 

Some books start off with a zero term and call it the first term of the 

sequence; other books start off with a term 1 as their first term

 

I will show both solutions:

 

a₆ = 5(5)^{(6 -1 )}    ;   a₇ = 5(5)^{( 7 - 1 )}

 

a₆ =5(5^{5)            ;}   a₇ = 5(5⁶)

 

a₆ = 15625         ;   a₇ = 78125

 

It just depends if you are looking at terms:  0, 1, 2, 3 , 4,.....

                                                or at terms: 1, 2, 3, 4, ..

Answer 2

a_n= 5(5)^n-1

a₇ = 5(5)^7-1

a₇ = 5(5)⁶

a₇ = 5⁷

a₇ = 78,125