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Paul [167]
3 years ago
14

What is the nth term?

Mathematics
1 answer:
kumpel [21]3 years ago
7 0

Let a_k denote the <em>k</em>th term of the sequence. Then

a_k=a_1+d(k-1)

where <em>d</em> is the common difference between consecutive terms in the sequence and <em>a</em>₁ is the first term.

The sum of the first <em>n</em> terms is

S_n=\displaystyle\sum_{k=1}^na_k=a_1+a_2+\cdots+a_{n-1}+a_n

From the formula for a_k, we get

S_n=\displaystyle\sum_{k=1}^n(a_1+d(k-1))=a_1\sum_{k=1}^n1+d\sum_{k=1}^n(k-1)

S_n=\displaystyle na_1+d\sum_{k=0}^{n-1}k

S_n=na_1+\dfrac{d(n-1)n}2

S_n=\dfrac n2(2a_1-d+dn)

So we have d=-5, and 2a_1-d=16 so that a_1=\frac{11}2.

Then the <em>n</em>th term in the sequence is

a_n=\dfrac{11}2-5(n-1)=\boxed{\dfrac{21-10n}2}

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Step-by-step explanation:

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3 years ago
Answer this question:What is the difference between 9 &lt; x and 9 = x? Explain.
maw [93]

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3 0
3 years ago
F(x) = ax2 - 12, g(x) = 2x +3, and f(3) = 24. What<br> is the value of g(f(2)) ?
elixir [45]
<h2>Answer:    g(f(2))  = 11</h2>

Step-by-step explanation:

g(f(2)) is substituting the value of f(2) for x in g(x). But we must first find f(2).

We know that f (x) = ax² - 12

Since f(3) = 24

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       9 a  = 36

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         =  4

 

⇒ g(f(2)) = 2(4) + 3

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6 0
2 years ago
Read 2 more answers
The given line passes through the points (-1,-1) and (4.1).
ira [324]

Answer:

(-1,-1) and (4.1).

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(y-3) = -5/2(x+1)

6 0
3 years ago
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