Mathematics, 20.02.2020 06:31 naomihiggins4033

The first two terms of a sequence are a1=4 and a2=-2. Let a3 be the third term when the sequence is arithmetic and let b3 be the third term when the sequence is geometric. Find a3+b3

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Answer from: tcarston1728

a_3=-8 ; b_3=1

Therefore,

a_3+b_3=-8+1=-7

Step-by-step explanation:

Considering the first two terms of a sequence

$a_1=4\:;\:a_2=-2$

Finding a_3 when the sequence is arithmetic

Let a_3 be the third term when the sequence is arithmetic.

The common difference = d = -2 - 4 = -6

The n-th term of Arithmetic sequence is:

$a_n=a_1+\left(n-1\right)d$

Putting n = 3 in the n-th term to find a_3 .

$a_n=a_1+\left(n-1\right)d$

$a_3=4+\left(3-1\right)\left(-6\right)$

a_3=4-12

a_3=-8

Finding b_3 when the sequence is geometric

Let b_3 be the third term when the sequence is geometric.

The common ratio r is:

$r=-\frac{2}{4}=-\frac{1}{2}$

The n-th term of a geometric sequence with initial value b and common ratio r is given by

$b_{n}=b\,r^{n-1}$

Putting n = 3 in the n-th term to find b_3 .

$b_3=4\cdot \left(-\frac{1}{2}\right)^{3-1}$

$b_3=4\cdot \frac{1}{2^2}$ ∵ $\left(-\frac{1}{2}\right)^{3-1}=\frac{1}{2^2}$

$b_3=\frac{1\cdot \:4}{2^2}$

$b_3=\frac{2^2}{2^2}$

b_3=1

So,

a_3=-8 ; b_3=1

Therefore,

a_3+b_3=-8+1=-7

Answer from: Quest

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Answer from: Quest

the number of the people going.

step-by-step explanation:

the cost to buy one movie ticket is $7. if the total cost for the movie is a function of how many people go, then the input is : the number of the people going.

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The first two terms of a sequence are a1=4 and a2=-2. Let a3 be the third term when the sequence is...

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