How do you find the nth term of the sequence −1,2,−3,4,−5,6,...?

inhiba5f
2022-09-13
Answered

How do you find the nth term of the sequence −1,2,−3,4,−5,6,...?

You can still ask an expert for help

Hofpoetb9

Answered 2022-09-14
Author has **17** answers

We have a sequence:

−1,2,−3,4,−5,6,...

Firstly we note that the absolute value of the terms increment by unity. so we can denote the absolute value as:

1,2,3,4,5,6,...

So we can denote the absolute value of the $n}^{th$ term by n

Secondly, we note that the signs of each term alternates, and we start with a negative term

$-,+,-,+,...$

And we can achieve the correct sign for the $n}^{th$ term by $(-1)}^{n$

Hence we can denote the $n}^{th$ term of the sequence by:

${u}_{n}={(-1)}^{n}n$

−1,2,−3,4,−5,6,...

Firstly we note that the absolute value of the terms increment by unity. so we can denote the absolute value as:

1,2,3,4,5,6,...

So we can denote the absolute value of the $n}^{th$ term by n

Secondly, we note that the signs of each term alternates, and we start with a negative term

$-,+,-,+,...$

And we can achieve the correct sign for the $n}^{th$ term by $(-1)}^{n$

Hence we can denote the $n}^{th$ term of the sequence by:

${u}_{n}={(-1)}^{n}n$

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Give the first six terms of the following sequences.

1)${g}_{1}=2$ and ${g}_{2}=1$

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3)${b}_{1}=1,{b}_{2}=3$ and $b}_{n}={b}_{n-1}-{b}_{n-2$ for $n\ge 3$

4)${d}_{1}=1,{d}_{2}=1$ and $d}_{n}={\left({d}_{n-1}\right)}^{2}+{d}_{n-2$ for $n\ge 3$

1)

2)

3)

4)

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(a) How many sequences contain exactly two heads?

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(a) How many sequences contain exactly two heads?

(b) Probability extension: Assuming the sequences are all equally likely, what is the probability that you will get exactly two heads when you toss a coin three times?