Question 774396
each of my five digits is one more than the digit to its left.the sum of my digits is 20.what number am i ?


Let ten-thousands digit be T 
Then thousands digit = T + 1
Hundreds digit = T + 1 + 1, or T + 2
Tens digit = T + 2 + 1, or T + 3
Units digit = T + 3 + 1, or T + 4
 

Therefore, T + T + 1 + T + 2 + T + 3 + T + 4 = 20
5T + 10 = 20
5T = 20 – 10


T, or tens-thousands digit = {{{10/5}}}, or 2
Thousands digit = 2 + 1, or 3
Hundreds digit = 3 + 1, or 4
Tens digit = 4 + 1, or 5
Units digit = 5 + 1, or 6


Five-digit number: {{{highlight_green(23456)}}}


OR Solve using the sum of an arithmetic series: {{{S[n] = (n/2)(a[1] + (n - 1)d)}}} ----- {{{S[5] = (5/2)(a[1] + (5 - 1)1)}}}. Solve for {{{a[1]}}} or the 1st term (ten-thousands digit), and then calculate other digits/terms.


You can do the check!! 


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