Trixie wants to create an especially tricky arithmetic sequence. she wants the 5th term of the sequence to equal 11 and the 50th term to equal 371. that is, she wants t(5) = 11 and t(50) = 371. is it possible to create an arithmetic sequence to fit her information? if it is possible, find the rule, the initial value t(0), and the common difference for the arithmetic sequence. if it is not possible, explain why not.

-21, - 13, - 5, 3, 5, ....

using the nth term formula for an arithmetic sequence

= + (n - 1)d

we require to find and d

= + 4d → (1)

= + 49d → (2)

subtract equation (1) from equation (2)

45d = 360 ⇒ d = = 8

substitute d = 8 into equation (1)

+ 32 = 11

= 11 - 32 = - 21

- 21, - 13, - 5, 3, 11 are the first 5 terms of the required sequence.

the first one

step-by-step explanation:

just id the test.

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.