In this worksheet, we will practice writing explicit and recursive formulas for arithmetic sequences.

**Q5: **

Consider the following growing pattern, shown for , , and .

Write an expression for the number of dots in the th such pattern.

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**Q6: **

The arithmetic mean between the third and seventh term of a sequence is 36 and the tenth term exceeds the double of the fourth term by 6. Find the general term, , of the arithmetic sequence.

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**Q7: **

Find the general term of the arithmetic sequence which satisfies the relations and .

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**Q8: **

A cable television offers its service at $45 per month and a one-time setup fee of $19.95. Express the total amount paid after months by a recursive formula.

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**Q9: **

Find the sequence and its general term of all the even numbers greater than 62.

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- D ,

**Q10: **

Find, in terms of , the general term of the sequence .

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**Q11: **

Find, in terms of , the general term of the sequence .

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**Q12: **

Engy started working out to get healthier. She worked out for fourteen minutes on the first day and increased her exercise by six minutes every day. Find, in terms of , the term of the sequence which represents her plan.

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**Q13: **

The graph represents the triangle wave function , which is periodic, piecewise linear, and defined for all real numbers.

Let be the th positive solution to the equation . Starting from , write a recursive formula for .

- A for .
- B for .
- C for .
- D for .
- E for .

What is the set of numbers which satisfy the equation

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The part of the graph through the origin coincides with the line . Use this to find one solution to . Use the symmetries of the graph to find the next positive solution.

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Find the first two positive solutions to .

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Find the value of , giving your answer correct to 3 decimal places.

**Q20: **

The arithmetic mean between the third and seventh term of a sequence is and the tenth term exceeds the double of the fourth term by 44. Find the general term, , of the arithmetic sequence.

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**Q21: **

Find the general term of the arithmetic sequence which satisfies the relations and .

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