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2 years ago

What is the recursive rule for this geometric sequence? 7, 21, 63, 189,…

Mathematics

1 answer:

Marysya12 [62]2 years ago

4 0

Answer:

The top choice is the answer. a1=7; an= 3*a_(n-1)

Step-by-step explanation:

Begin by finding out what the terms are multiplied by. It is a geometric sequence so multiplication is involved.

Take the 3rd term (63) and divide it by the second term.

63/21 = 3

What this means is that each term in the sequence is multiplied by 3 to get to the next term.

The first term is 7

So the answer is an = 3* a_n-1

The answer must be the top one. See if it works.

a2 = 3*a_(2 -1 )

a2 = 3 * a1

a2 = 3 * 7

a2 = 21 which it does.

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There are 620 students and 31 teachers at the Turner Middle School.There are 950 students and 38 teachers at the Green Middle Sc

kicyunya [14]

We begin with the Turner Middle School:
Ratio of students to teachers: $\frac{620}{31}$
Green Middle School:
Ratio of students to teachers: $\frac{950}{38}$
Let check that we cannot form a proportion:
$\frac{620}{31}=20\text{ and } \frac{950}{38}=25$
The two ratios are not equals so we cannot form a proportion.
Let x be the number of teachers that Green have to hire in order to make the two ratios equal. We get the equation:
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Part-to-whole ratio:
Turner Middle School:
$\frac{620}{31+620}$
Green Middle School:
$\frac{950}{38+950}$

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