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 ?
Found 2 solutions by DrBeeee, MathTherapy:
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! What you are dealing with is the sum of the first n integers from 1 to n or let
(1) Sn = 1 + 2 + 3 + 4 + ... + n
You can figure out your answer by trial and error (the hard way).
(2) if n = 3; S3 = 1 + 2 + 3 = 6
(3) if n = 6; S6 = 1 + 2 + 3 + 4 + 5 + 6 = 21
You want the sum to be equal to 20 so start at 2 instead of 1 and get
(4) 20 = 2 + 3 + 4 + 5 + 6
Not too hard but not very mathematical. So let me give you a little lesson on sums
given by (1). The formula for (1) is
(5) Sn = n*(n+1)/2
Let's try it for n = 3,
(6) S3 = 3*(3+1)/2 or
(7) S3 = 3*4/2 or
(8) S3 = 6 as given by (2).
Let's try it for n = 6,
(9) S6 = 6*(6+1)/2 or
(10) S6 = 6*7/2 or
(11) S6 = 21 as given by (3).
How about the sum of 1 to 100? Want to add them up or use (5)? While you add I'll use (5) to get
(12) S100 = 100*101/2 or
(13) S100 = 5050
Easy isn't it? Please remember this formula, it will come in handy when you study probability.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! 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 =  , 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: 
OR Solve using the sum of an arithmetic series:  -----  . Solve for  or the 1st term (ten-thousands digit), and then calculate other digits/terms.
You can do the check!!
Further help is available, online or in-person, for a fee, obviously. Send comments, “thank-yous,” and inquiries to “D” at MathMadEzy@aol.com
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