Question

Find the mean of this sequence 5, 25, 125, 625, 3125 and state of it a Arithmetic or Geometric Progressions.

Answer 1

$\purple{Hey \: mate \: }$

S(5)=3125

PREMISES

S=5,25,125,625,…

CALCULATIONS

S=5,25,125,625,…

By inspection, the “partial” sequence S=5,25,125,625… shows a set of distinct “whole” numbers that appear to follow a discernible pattern, or order, where the numbers (terms) increase by powers of 5.

ALGORITHM

S(n)=5^n, where 5=a constant base (base-10) and where n=every nth term of the sequence, i.e., n1=term #1, n2= term #2, n3=term #3.

PATTERN

(1) 5^1=5

(2) 5^2=25

(3) 5^3=125

(4) 5^4=625

(5) 5^5=3,125 [ANSWER]

(6) 5^6=15,625

(7) 5^7=78,125

(8) 5^8=390,625

(9) 5^9=1,953,125

(10) 5^10=9,765,625

(100) 5^100=7.888609052210118E +69

(1,000) 5^1,000=most calculators display “I nf inity”

C.H.