# Worksheet: Explicit and Recursive Formulas of Arithmetic Sequences

Q1:

The fifth term of an arithmetic sequence is 50 and the tenth term is 25 times greater than the second term. Find the general term .

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Q2:

The fifth term of an arithmetic sequence is and the tenth term is 2 times greater than the second term. Find the general term .

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Q3:

The fifth term of an arithmetic sequence is 210 and the tenth term is 3 times greater than the second term. Find the general term .

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Q4:

Find, in terms of , the general term of an arithmetic sequence whose sixth term is 46 and the sum of the third and tenth term is 102.

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Q5:

Find, in terms of , the general term of an arithmetic sequence whose ninth term is and sixteenth term is .

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Q6:

Find, in terms of , the general term of an arithmetic sequence whose sixth term is and the sum of the third and tenth term is .

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Q7:

The fifth term of an arithmetic sequence is 4 and the tenth term is times greater than the second term. Find the general term .

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Q8:

Find, in terms of , the general term of an arithmetic sequence whose sixth term is 30 and the sum of the third and tenth term is 67.

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Q9:

Find, in terms of , the general term of an arithmetic sequence whose ninth term is 478 and sixteenth term is 891.

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Q10:

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.

Q11:

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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Q12:

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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Q13:

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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Q14:

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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Q15:

The third term in an arithmetic sequence is 2 and the sixth term is 11. If the first term is , what is an equation for the th term of this sequence?

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Q16:

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

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Q17:

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

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Q18:

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

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Q19:

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

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Q20:

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

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Q21:

Jennifer 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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