Math, asked by badatmath101, 6 months ago

Consider the sequence of numbers: , , 1StartFraction 3 Over 8 EndFraction, StartFraction 3 Over 4 EndFraction, 1 and StartFraction 1 Over 8 EndFraction, 1 and StartFraction 1 Over 8 EndFraction, 1 and StartFraction 7 Over 8 EndFraction. . ., 1 , 1, . . . Which statement is a description of the sequence?

Answers

Answered by 35majerczyk
24

Answer:

The sequence is recursive and can be represented by the function f(n + 1) = f(n) + 3/8

Step-by-step explanation: i got it right in edgenuity right now.

Answered by smithasijotsl
0

Answer:

The statement describing the sequence =  \frac{3}{8}n

Step-by-step explanation:

Given

The sequence of fractions is

\frac{3}{8},\frac{3}{4},1\frac{1}{8},1\frac{4}{8},1\frac{7}{8},...................

To find,

A statement describing this sequence

Recall the formula

The nth term of an AP is a+(n-1)d, where 'a' is the first term and 'd' is the common difference.

Solution

Given fraction is

\frac{3}{8},\frac{3}{4},1\frac{1}{8},1\frac{4}{8},1\frac{7}{8},...................

= \frac{3}{8},\frac{3}{4},\frac{9}{8},\frac{12}{8},\frac{15}{8},...................

Here the first term of the sequence is \frac{3}{8},

The second term is \frac{3}{4} = \frac{6}{8}

The third term is \frac{9}{8}

second term -  first term = \frac{6}{8} - \frac{3}{8}  = \frac{3}{8}

Third term - second term = \frac{9}{8} - \frac{6}{8}  = \frac{3}{8}

∵Third term - second term  = second term -  first term,

The given sequence form an AP, with the first term \frac{3}{8} and common difference  \frac{3}{8}

n-th term =  \frac{3}{8} + (n-1) \frac{3}{8}

= \frac{3}{8} +  \frac{3}{8}n - \frac{3}{8}

= \frac{3}{8}n

∴ The statement describing the sequence is  \frac{3}{8}n, where 'n' is a natural number.

#SPJ3

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