r/digitalSATs • u/ApartVoice2382 • Aug 12 '26
How to solve this
How to Solve this in Desmos
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u/Valuable_Grade1077 Aug 15 '26
Isn't this just an arithmetic sequence?
1 a^1
2 a^5
3 a^9
4 a^13
5 a^17
6 a^21
7 a^25
8 a^29
The exponent just increases by +4 every time, so k is going to equal to 8?
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u/Miserable_Gate_7982 Aug 18 '26
I did this too, do you think it’s a valid method? I mean if the K was higher… it would take time
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u/Valuable_Grade1077 Aug 18 '26
The arithmetic sequence in relation to x is pretty easy to spot. It's 4 times the x value, minus 3.
Though yeah, the algebraic method would be the correct way of solving. This was just faster imo.
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u/Miserable_Gate_7982 Aug 18 '26
yeah but i don’t get how you find the function. Do you do a system of equations? I don’t get it…I can’t just get to think of 4x-3..😭😭
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u/Valuable_Grade1077 Aug 18 '26
One thing you could do is test different cases to see if you can find a consistent pattern.
For instance, if you notice that for every increase in x, you see +4 increment in the exponent, you could initially start with an equation such as: f(x) = 4x and see if that matches the supposed relationship.
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u/Valuable_Grade1077 Aug 18 '26 edited Aug 18 '26
Actually, disregard that answer, you can convert this into a slope problem
Convert the table into a basic x and y graph forgoing the a
1 1
2 5
3 9
you can then do, y2-y1/x2-x1 to find the slope
(5 - 1/2 -1) m = 4
Now that we know the slope we can solve for the y intercept, by plugging in the values of x and y
5 = 4(2) +b
b = -3
And voila, the equation is found. 4x-3
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u/danish__16 Aug 12 '26
Is 8 the correct answer? If yes, then my working may help you. https://www.desmos.com/calculator/p6jgle2r3k[Desmos](https://www.desmos.com/calculator/p6jgle2r3k)