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
