The third term of the sequence is 120. The fifth term is 76.8 The explicit rule for the geometric sequence is an=?(?)n-1

The explicit rule of the geometric sequence

 aₙ   = 187.5 (0.8)ⁿ⁻¹

Step-by-step explanation:

Step(i):-

Given that the third term of the sequence = 120

        tₙ = a rⁿ⁻¹  

       t₃  = a r³⁻¹ = ar²

        120 = ar² ..(i)

Given that the fifth term of the given geometric sequence = 76.8

        tₙ = a rⁿ⁻¹  

       t₅  = a r⁵⁻¹ = a r⁴

   76.8  = a r⁴...(ii)

Step(ii):-

 Dividing (ii) and (i)

        r²   = 0.64

       r    =√ 0.64 = 0.8

Substitute r= 0.8 in equation (i)

         120 = ar²

       120 = a(0.8)²

⇒      

Step(iii):-

The explicit rule of the geometric sequence

                 aₙ  = a rⁿ⁻¹

put a= 187.5  and r = 0.8

                aₙ   = 187.5 (0.8)ⁿ⁻¹

step-by-step explanation:

here's what happens:

1) the graph of f   = x^2 is shifted 2 units to the right.

2) the resulting graph is reflected in the x-axis, so that the parabola now opens down.

3) this final result is transformed up by 5 units.

b. 1.25 hr

step-by-step explanation:

if you have a constant speed of 60 mph, then you have a ratio between 60 mi. to 1 hr. dividing both sides by 60 we get the ratio

1 mi. to

then mult. both sides by 75 we get the ratio

75 mi. to

simplifying we get

75 mi. to

or 1.25 hr.