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slega [8]
2 years ago
7

What is the nth term rule of the linear sequence below?

Mathematics
1 answer:
aleksklad [387]2 years ago
4 0

Answer:

a_n=5+2n

Step-by-step explanation:

Each term is 2 more than the previous term, so the common difference is 2.

Let a_n be the nth term of the sequence. Then, the first term is a_1=7.

The second term is a_2=7+2=9, and the third term is a_3=7+2+2=11.

Therefore, every term can be written as

a_n=7+\underbrace{2+2\cdots +2}_{n-1~\text{times}}.

Since repeated addition is multiplication, this can be written as

a_n=7+2(n-1),

which is the nth term rule of the linear sequence.

This could also be expanded to \boxed{a_n=5+2n.}

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The sum of the first three terms of an arithmetic sequence is 108, and the sum of the next three terms is 183. what is the value
qaws [65]
The key is to find the first term a(1) and the difference d.

in an arithmetic sequence, the nth term is the first term +(n-1)d
the firs three terms: a(1), a(1)+d, a(1)+2d
the next three terms: a(1)+3d, a(1)+4d, a(1)+5d,
a(1) + a(1)+d +a(1)+2d=108
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subtract the first equation from the second equation: 9d=75, d=75/9=25/3
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the 11th term is: a(1)+(25/3)(11-1)=83/3 +250/3=111

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4 0
3 years ago
The graph of a quadratic function passes through the points (-1,0), (-2,0), and (0,2). Write the quadratic function in general f
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Answer:

Step-by-step explanation:

You have 3 points and need to find ax2 + bx + c = y. First use (0,2). x is zero, so y = 2 = c. You have c. Now put (-1,0) into the equation. 0 = 1a -b + 2. Rearrange so you get b = a + 2. Now use the other point. a*(-2 squared) + b*(-2) + 2 = 0. Simplify and substitute (a + 2) for b and you will have the answer.

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Answer:

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Hope this helps:)!

5 0
2 years ago
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