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mihalych1998 [28]
3 years ago
10

Find the third, fourth, and fifth terms of the sequence defined by

Mathematics
2 answers:
statuscvo [17]3 years ago
7 0

By the recursive definition,

a_3=2a_2-a_1=2\cdot9-4=14

a_4=2a_3-a_2=2\cdot14-9=19

a_5=2a_4-a_3=2\cdot19-14=24

a_6=2a_5-a_4=2\cdot24-19=29

olga_2 [115]3 years ago
7 0

Answer:

  a3=14, a4=19, a5=24

Step-by-step explanation:

Put the numbers where the symbols are and do the arithmetic.

  a3 = 2(a2) -(a1) = 2(9) -4 = 14

  a4 = 2(a3) -(a2) = 2(14) -9 = 19

  a5 = 2(a4) -(a3) = 2(19) -14 = 24

  a6 = 2(a5) -(a4) = 2(24) -19 = 29

_____

With a little work, you can show that this is an arithmetic sequence with a common difference of a2-a1 = 5.

Let d = a[2] -a[1]

Of course, the second term is that difference added to the first:

  a[2] = a[1] + (a[2] -a[1]) = a[1] +d

The third term is ...

  a[3] = 2a[2] -a[1] = a[2] +(a[2] -a[1]) = a[2] +d

  a[4] = 2a[3] -a[2] = a[3] +(a[3] -a[2]) = a[3] -(a[2] +d) -a[2] = a[3] +d

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Since the constant has been moved to the left side, you can move on to the next step which is adding (b/2)² to both sides of the equation.

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Step-by-step explanation:

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The number of nickels saved on day n is 2^n. The total is 2^(n+1)-2.

_____

The above can be written down from your knowledge of binary sequences. If you want a more formal development, read on.

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