ruigE

2021-08-21

Consider the following sequences
1)${a}_{n}=-2,5,12,19,\dots$
2)${b}_{n}=3,6,12,24,48\dots$
Find the next two terms of the sequence
Find a recurrence relation that generates the sequence
Find an explicit formula for the nth term of the sequence

irwchh

1)
Given sequence in an airthematic sequence
First term, ${a}_{1}=-2$
Common difference, $d=5-\left(-2\right)=5+2=7$
Next two terms are ${a}_{5}={a}_{1}\left(5-1\right)d=-2+\left(4\right)7=-2+28$
${a}_{5}=26$
${a}_{6}={a}_{1}\left(6-1\right)d=-2+\left(5\right)7=-2+35$
${a}_{5}=33$
Recurrence formula
${a}_{1}=-2$
${a}_{n}={a}_{n-1}+7$
Explicit formula
${a}_{5}={a}_{1}\left(n-1\right)d$
2)
Given sequence is a multiple of 2
First term ${a}_{1}=3$
${a}_{6}=2{a}_{5}=2\left(48\right)=96$
${a}_{7}=2{a}_{6}=2\left(96\right)=192$
Recurrence formula
${a}_{1}=3$
${a}_{n}=2{a}_{n-1}$
Explicit formula ${a}_{n}=3{\left(2\right)}^{n-1}$

Do you have a similar question?

Recalculate according to your conditions!
The text passage contains a mathematical problem involving two sequences, with questions about finding the next terms, recurrence relations, and explicit formulas. Answers to these questions are provided for both sequences.
multiple_questions_with_answers
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
ruigE

2021-08-21

Consider the following sequences
1)${a}_{n}=-2,5,12,19,\dots$
2)${b}_{n}=3,6,12,24,48\dots$
Find the next two terms of the sequence
Find a recurrence relation that generates the sequence
Find an explicit formula for the nth term of the sequence

irwchh

1)
Given sequence in an airthematic sequence
First term, ${a}_{1}=-2$
Common difference, $d=5-\left(-2\right)=5+2=7$
Next two terms are ${a}_{5}={a}_{1}\left(5-1\right)d=-2+\left(4\right)7=-2+28$
${a}_{5}=26$
${a}_{6}={a}_{1}\left(6-1\right)d=-2+\left(5\right)7=-2+35$
${a}_{5}=33$
Recurrence formula
${a}_{1}=-2$
${a}_{n}={a}_{n-1}+7$
Explicit formula
${a}_{5}={a}_{1}\left(n-1\right)d$
2)
Given sequence is a multiple of 2
First term ${a}_{1}=3$
${a}_{6}=2{a}_{5}=2\left(48\right)=96$
${a}_{7}=2{a}_{6}=2\left(96\right)=192$
Recurrence formula
${a}_{1}=3$
${a}_{n}=2{a}_{n-1}$
Explicit formula ${a}_{n}=3{\left(2\right)}^{n-1}$

Do you have a similar question?

Recalculate according to your conditions!
user
The text passage contains a mathematical problem involving two sequences, with questions about finding the next terms, recurrence relations, and explicit formulas. Answers to these questions are provided for both sequences.

TYPE: MULTIPLE_QUESTIONS_WITH_ANSWERS