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PtichkaEL [24]
3 years ago
8

Find a general term an for the sequence whose first four terms are given. 2, 4, 8, 16, ...

Mathematics
1 answer:
lapo4ka [179]3 years ago
7 0

Answer:

  an = 2·2^(n-1)

Step-by-step explanation:

There are simple tests to determine whether a sequence is arithmetic or geometric. The test for an arithmetic sequence is to check to see if the differences between terms are the same. Here the differences are 2, 4, 8, so are not the same.

The test for a geometric sequence is to check to see if the ratios of terms are the same. Here, the ratios are ...

  4/2 = 2

  8/4 = 2

  16/8 = 2

These ratios are all the same (they are "common"), so the sequence is geometric.

The general term of a geometric sequence with first term a1 and common ratio r is ...

  an = a1·r^(n-1)

Filling in the values for this sequence, we find the general term to be ...

  an = 2·2^(n-1)

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Step-by-step explanation:

8 0
2 years ago
Javier's parents set an amount of money aside when he was born. They earned 4.5% simple interest on that money each year. When J
solmaris [256]

Answer:

Javier's parents set aside $1500 when he was born

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

E = P*I*t

In which E is the interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

In this question, we have that:

E = 1012.50, t = 15, I = 0.045

We have to find P. So

E = P*I*t

1012.50 = P*15*0.045

P = \frac{1012.50}{15*0.045}

P = 1500

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6 0
2 years ago
help please !!!Kevin wants to make a mixture that is 50% lemon juice and 50% lime juice. How much 100% lemon juice should he add
Liula [17]
So basically, he wants to make mixture where lemon=lime

it is 6 gallons so
40% of 6=0.4 times 60=2.4=lemon
60% of 6=0.6 times 60=3.6=lime
so to make them equal
3.6-2.4=1.2
he must add 1.2 gallons of 100% lemon juice to make a mixture of 50% lemon and 50% lime

1.2 gallons is the answer
8 0
3 years ago
Solve the “and” compound inequality for –1 < 6x + 1 ≤ 13
ser-zykov [4K]

Answer:

-1/3 < x <(or equal to) 2

Step-by-step explanation:

Firstly divide your inequality into two separate inequalities...

1) -1 < 6x + 1...then solve for the first one..,which then gives you....;

-2 < 6x....which gives us our first solution (x > -1/3)

Then the second inequality

2) 6x + 1 <(or equal to) 13

which then gives you....,

6x <(or equal to) 12...which then gives our second solution...( x <(or equal to) 2)

Then combine the two solutions into a compound solution

-1/3 < x <(or equal to) 2

8 0
3 years ago
A2 - b2 - 2a + 1 plss give me answer fast
mario62 [17]

Answer:

( a − 1 + b )( a − 1 − b )

.

6 0
3 years ago
Read 2 more answers
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