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Arithmetic Sequences (Easy)

AMC 10 Q1–8 depth — contest entry, not school drills.

Easy Medium Hard AIME / USAJMO / AMO

Arithmetic Sequences: core idea

a_n

formula.

Example problem: hint and answer

Find the next term: $3,7,11,15,\ldots$ .

Hint: Use $a_n=a_1+(n-1)d$ . Answer: 19.

Practice (9 problems — type your answers)

1. Find the common difference of $10,16,22,\ldots$ .
2. Find the $10$ th term of $2,5,8,\ldots$ .
3. Find the first term if $a_5=21$ and $d=4$ .
4. Find $a_7$ if $a_1=9$ and $d=-2$ .
5. Find the sum of $1+2+3+\cdots+10$ .
6. How many terms are in $4,7,10,\ldots,31$ ?
7. Find the average of the first and last terms of $8,11,\ldots,29$ .
8. Find $a_1$ if $a_8=30$ and $d=3$ .
9. Find the sum $5+10+15+\cdots+50$ .

Arithmetic Sequences Practice Problems — Easy