Sequence Rule Finder

Intro: Given the first few terms, checks differences and ratios to decide if a sequence is arithmetic or geometric, then finds aₙ.

Worked example

• The sequence is 3, 7, 11, 15, ... Determine if it is arithmetic or geometric and find aₙ.



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• We list the given terms: $a_1=3$, $a_2=7$, $a_3=11$, $a_4=15$.



• Check for arithmetic pattern by computing differences: $a_2-a_1 = 7-3=4$, $a_3-a_2=11-7=4$, $a_4-a_3=15-11=4$.



• Since the differences are constant (4), the sequence is arithmetic with common difference $d=4$.



• The general form of an arithmetic sequence is $a_n = a_1 + (n-1)d$.



• Here $a_1=3$ and $d=4$, so $a_n = 3 + (n-1)\cdot4$.



• Simplify: $a_n = 3 + 4n - 4 = 4n - 1$.



• We can check with $n=4$: $a_4 = 4\cdot4-1=15$, which matches the given term.



• Answer: $\boxed{\text{Arithmetic with } d=4,\; a_n=4n-1.}$

Why choose MathGPT?

• Get clear, step-by-step solutions that explain the “why,” not just the answer.
• See the rules used at each step (power, product, quotient, chain, and more).
• Optional animated walk-throughs to make tricky ideas click faster.
• Clean LaTeX rendering for notes, homework, and study guides.

How this calculator works

• Type or paste your function (LaTeX like \sin, \ln works too).
• Press Generate a practice question button to generate the derivative and the full reasoning.
• Review each step to understand which rule was applied and why.
• Practice with similar problems to lock in the method.

Related

• Arithmetic & Geometric Series
• Function Rule from Table