Question

Which formula can be used to find the nth term of a geometric sequence where the fifth term is 1/16 and the common ratio is 1/4 ?

Answer 1

Answer:

a₅ = 16(1/4)⁴

Step-by-step explanation:

Answer 2

A₅ = 1/16  and r= 1/4

Let see how to build up this formula that is going to give that term of rank n

1st term =a₁ = To be calculated

1st a₁   = a₁  x  r°
2nd a₂  = a₁  x  r¹
3rd a₃  =  a₁  x  r²
4th a₄   = a₁  x  r³
5th a₅   = a₁  x  r⁴
.......................
.......................
nth : a(n) = a₁  x r⁽ⁿ-¹)
Note when that the subscript of a is the same as the exponent mines 1

We know the ratio r =1/4 & the fifth term, a₅ =1/16 (given). Now let's apply the formula to calculate the unknown a₁.

a(n) = a₁  x r⁽ⁿ-¹) ==>a₅ = a₁ x (1/4)⁽⁵⁺¹⁾ ===> 1/16 = a₁ x (1/4)⁴
1/167 = a₁ (1/256) ==> a₁ =16 & the formula becomes
a₅ = 16(1/4)⁴