Question

What is the next fraction in each of the following patterns? a. 1⁄40, 4⁄40, 9⁄40, 16⁄40, 25⁄40 . . .? b. 3⁄101, 4⁄101, 7⁄101, 11⁄101, 18⁄101, 29⁄101. . .? c. 5⁄1, 10⁄2, 9⁄2, 18⁄4, 17⁄8, 34⁄32, 33⁄256. . .?

Answer 1

a) 36 
b) 47
c) 8,192

a. 1*1=1,2*2=4,3*3=9,4*4=16,5*5=25,6*6=36
b. 3+4=7,4+7=11,7+11=18,11+18=29,18+29=47
c. 1*2=2,2*2=4,2*4=8,4*8=32,8*32=256,32*256=8,192

Answer 2

The next terms are 36/40, 47/101, and 66/8192 for part (a), part (b), and part (c) respectively.

What is a sequence?

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have some of the sequences given:

a. 1⁄40, 4⁄40, 9⁄40, 16⁄40, 25⁄40 . . .

The denominator is the same for each term:

The numerator is the square of natural numbers

So the next term = 36/40

b. 3⁄101, 4⁄101, 7⁄101, 11⁄101, 18⁄101, 29⁄101. . .

The denominator is the same for each term:

The numertor is the sum of two previous terms:

The next term is = (18+29)/101 = 47/101

c. 5⁄1, 10⁄2, 9⁄2, 18⁄4, 17⁄8, 34⁄32, 33⁄256. . .

The denominator of the alternative terms is the multiplication of the denominator of the preceding two terms, and both terms increase by a multiple.

The next term = 66/8192

Thus, the next terms are 36/40, 47/101, and 66/8192 for part (a), part (b), and part (c) respectively.

Learn more about the sequence here:

brainly.com/question/21961097

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