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Eva8 [605]
3 years ago
10

Need help on 15 and 16 PLEASEE!!!

Mathematics
1 answer:
melisa1 [442]3 years ago
4 0

Answer:

Part 15) The next three terms are 5/8,3/4 and 7/8

Part 16) The 37th term is -35.5

Step-by-step explanation:

we know that

In an <u>Arithmetic Sequence</u> the difference between one term and the next is a constant and this constant is called the common difference (d)

Part 15) Find the next three terms of the arithmetic sequence

\frac{1}{8},\frac{1}{4},\frac{3}{8},\frac{1}{2},...

so

a1=1/8\\ a2=1/4\\ a3=3/8\\ a4=1/2\\ a2-a1=1/4-1/8=1/8\\ a3-a2=3/8-1/4=1/8\\ a4=a3=1/2-3/8=1/8

The common difference is equal to

d=1/8

<u><em>Find the next three terms of the arithmetic sequence</em></u>

<u><em>Find a5</em></u>

a5=a4+d ----->a5=1/2+1/8=5/8

<u><em>Find a6</em></u>

a6=a5+d ----->a6=5/8+1/8=3/4

<u><em>Find a7</em></u>

a7=a6+d ----->a7=3/4+1/8=7/8

therefore

The next three terms are

5/8,3/4 and 7/8

Part 16) what is the 37th term of the arithmetic sequence

4.1,3,1.9,0.8,...?

so

a1=4.1\\ a2=3\\ a3=1.9\\ a4=0.8

a2-a1=3-4.1=-1.1\\ a3-a2=1.9-3=-1.1\\ a4=a3=0.8-1.9=-1.1

The common difference is equal to

d=-1.1

We can write an Arithmetic Sequence as a rule

an=a1+d(n-1)

substitute the values

an=4.1-1.1(n-1)

For n=37

substitute

a37=4.1-1.1(37-1)

a37=4.1-1.1(36)

a37=-35.5

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