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In this lesson, we will learn how to write explicit and recursive formulas for 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 π π .

Q2:

The fifth term of an arithmetic sequence is β 1 8 7 and the tenth term is 2 times greater than the second term. Find the general term π π .

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 π π .

Q4:

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

Q5:

Find, in terms of π , the general term of an arithmetic sequence whose ninth term is β 7 1 7 and sixteenth term is β 1 3 4 7 .

Q6:

Find, in terms of π , the general term of an arithmetic sequence whose sixth term is β 3 1 and the sum of the third and tenth term is β 6 7 .

Q7:

The fifth term of an arithmetic sequence is 4 and the tenth term is β 1 times greater than the second term. Find the general term π π .

Q8:

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

Q9:

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

Q10:

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

Let π π be the π th positive solution to the equation π ( π₯ ) = β 1 . Starting from π = 3 2 1 , write a recursive formula for π π .

What is the set of numbers which satisfy the equation π ( π₯ ) = 1 ?

The part of the graph through the origin ( 0 , 0 ) coincides with the line π¦ = 2 π₯ . Use this to find one solution to π ( π₯ ) = 1 2 . Use the symmetries of the graph to find the next positive solution.

Find the first two positive solutions to π ( π₯ ) = β 0 . 3 4 6 .

Find the value of π ( π ) 5 , 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 π ( π ) after π β₯ 0 months by a recursive formula.

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, π π , of the arithmetic sequence.

Q13:

The arithmetic mean between the third and seventh term of a sequence is β 9 3 and the tenth term exceeds the double of the fourth term by 44 Find the general term, π π , of the arithmetic sequence.

Q14:

Consider the following growing pattern, shown for π = 1 , π = 2 , and π = 3 .

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

Q15:

The third term in an arithmetic sequence is 2 and the sixth term is 11. If the first term is π 1 , what is an equation for the π th term of this sequence?

Q16:

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

Q17:

Find the general term of the arithmetic sequence which satisfies the relations π + π = β 3 0 6 8 and π Γ π = 5 2 5 7 9 .

Q18:

Find the general term of the arithmetic sequence which satisfies the relations π + π = 1 4 1 2 1 4 and π Γ π = 7 1 3 1 5 .

Q19:

Find, in terms of π , the general term of the sequence 3 5 0 + 1 2 , 3 5 0 + 1 3 , 3 5 0 + 1 4 , 3 5 0 + 1 5 , β¦ .

Q20:

Find, in terms of π , the general term of the sequence ( 4 4 , 7 0 , 9 6 , 1 2 2 , β¦ ) .

Q21:

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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