⁵ (3 A Number pattern has 75 as the first
The rule of the number pattern
Subtract 6 to get the next number
What will be the fifth number in the
sequence

9514 1404 393

  51

Step-by-step explanation:

The rule gives the sequence ...

  75, 69, 63, 57, 51, 45, ...

The 5th number in the sequence is 51.

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Alternate solution

The equation for the general term of an arithmetic sequence is ...

  an = a1 +d(n -1) . . . . . for first term a1 and common difference d

Your sequence has first term 75 and common difference -6, so the equation is ...

  an = 75 -6(n -1)

Then for n=5, the term is ...

  a5 = 75 -6(5 -4) = 75 -24 = 51

The 5th term is 51.

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.