Is Goblins free for teachers?

Yes. Goblins offers a generous free tier that includes 1 live feedback assignment per week, insights on student mastery and replays, and the ability to upload your own content. The Max plan adds unlimited assignments, superadaptive mode, grade exports, standards growth reports, and SSO/LMS integration, with per-student pricing for schools and districts.

How does Goblins work?

Three simple steps: (1) Share an assignment from thousands of standards-aligned topics using a share code. (2) Students speak and draw their thinking naturally, and Goblins responds with Socratic questioning that sounds just like their teacher. (3) Teachers get real-time formative insights showing what students struggle with and suggestions to inform instruction.

Does Goblins prevent cheating?

Yes. Goblins uses a purpose-trained AI model that evaluates cheating signals in real time. It can detect when students are copying answers, using external tools inappropriately, or not genuinely working through problems. Copy-pasting answers is also blocked.

Can I use my own voice with Goblins?

Yes. Teachers can record their voice and take a selfie to create a custom 3D avatar in about 30 seconds. Students then hear help in their own teacher's voice and see a familiar face, making the experience more personal and effective.

What math levels does Goblins cover?

Goblins covers math from Grade 5 through AP Calculus, including thousands of standards-aligned topics. Teachers can also upload their own content for custom assignments at any level.

Is Goblins FERPA compliant?

Yes. Goblins is FERPA and state compliant. Student data privacy and security are a top priority.

Does Goblins support English Language Learners?

Yes. Goblins supports 30+ languages so teachers don't have to translate every worksheet. It is especially helpful for ELL students who need accessible math instruction in their native language.

HS.F.7.c

(+) Translate between recursive and explicit formulas.

Example Problems

For the following explicit formula of the arithmetic sequence:

f(n) = 37 + 4n

What is the recursive formula of

f(n)

Given the following recursive formula for the arithmetic sequence:

f(1) = -10

and

f(n) = f(n - 1) + 12

What is the explicit formula for

f(n)

Given the following recursive formula for the geometric sequence:

f(1) = 7

and

f(n) = f(n - 1) \cdot (-2)

What is the explicit formula for

f(n)

Khan Academy Resources

Intro to arithmetic sequence formulas Arithmetic sequences review Explicit formulas for arithmetic sequences Geometric sequences review Converting recursive & explicit forms of arithmetic sequences Recursive formulas for arithmetic sequences Use arithmetic sequence formulas Use geometric sequence formulas Recursive formulas for arithmetic sequences Converting recursive & explicit forms of arithmetic sequences Recursive formulas for geometric sequences Evaluate sequences in recursive form Explicit formulas for geometric sequences Linear models word problems Converting recursive & explicit forms of geometric sequences Explicit formulas for arithmetic sequences Sequences and domain Intro to arithmetic sequences Sequences intro Sequences and domain Explicit & recursive formulas for geometric sequences Using recursive formulas of geometric sequences Worked example: using recursive formula for arithmetic sequence Converting recursive & explicit forms of arithmetic sequences Linear functions word problem: iceberg Using arithmetic sequences formulas Linear functions word problem: paint Using explicit formulas of geometric sequences Evaluating sequences in recursive form Converting recursive & explicit forms of geometric sequences Explicit formulas for arithmetic sequences Recursive formulas for arithmetic sequences

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