Question 1209569: 1 + 4 + 7 + 10 + ... + x = 287
find x
Found 4 solutions by josgarithmetic, ikleyn, math_tutor2020, greenestamps:
Answer by josgarithmetic(39630)   (Show Source):
Answer by ikleyn(52884)  (Show Source):
You can put this solution on YOUR website! .
1 + 4 + 7 + 10 + ... + x = 287
find x
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It is an anti-mathematical way to present a problem.
It makes me feel sick.
As well as any other person, who has a Math education and feeling of harmony . . .
Normal and standard " human " way (= right way) to formulate this problem mathematically is THIS
The sum of the first n terms of an arithmetic progression
with the first term 1 and the common difference 3 is 287.
Find the number of terms "n" and the value of the n-th term.
How the problem is presented in your post is  .
It reminds me of how the witch doctors stir the potion in cups,
in 700 years old tales.
Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!
Answer: x = 40
Explanation
1, 4, 7, 10, ... is an arithmetic sequence
a1 = 1 is the first term
d = 3 is the common difference.
Sn = sum of the first n terms
Sn = 0.5n*(2*a1+d*(n-1))
287 = 0.5n*(2*1+3*(n-1))
1.5n^2-0.5n-287 = 0
Using the quadratic formula will yield solutions n = -13.667 (approximate) and n = 14.
We ignore the negative value of n.
n must be a positive whole number 1,2,3,etc
I'll let the student handle the scratch work for the quadratic formula.
We determined there are 14 terms being added in {1,4,7,10,...,x} to yield the sum 287.
Let's determine the 14th term.
an = a1 + d(n-1)
an = 1 + 3*(n-1)
an = 3n-2
a14 = 3*14-2
a14 = 40
Therefore, x = 40 and 1+4+7+10+...+40 = 287
Verification using WolframAlpha
Another way to confirm is to use a spreadsheet.
Answer by greenestamps(13209)  (Show Source):
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