Q1: a_n=2n+3
Q2: The 12th term of sequence is 70
Step-by-step explanation:
Question No. 1
Given sequence is:
5,3,1,-1,-3....
Common difference is the difference between consecutive terms of an arithmetic sequence.
We have to find the common difference first
[tex]d=a_2-a_1=5-3=2\\a_3-a_2=3-1=2[/tex]
The first term is: 5
The general formula for arithmetic sequence is:
[tex]a_n=a_1+(n-1)d[/tex]
Putting the values of a1 and d
[tex]a_n=5+(n-1)(2)\\a_n=5+2n-2\\a_n=2n+3[/tex]
Question No. 2:
Given
[tex]a_7=40\\a_18=106[/tex]
According to general formula, the expression for 7th and 18th term is:
[tex]a_7=a_1+(7-1)d=>40=a_1+6d\ \ \ \ Eqn\ 1\\a_18=a_1+(18-1)d = >106=a_1+17d\ \ \ \ Eqn\ 2\\Subtracting\ Eqn\ 1\ from\ eqn\ 2\\a_1+17d-a_1-6d=106-40\\11d=66\\Dividing\ both\ sides\ by\ 11\\\frac{11d}{11}=\frac{66}{11}\\d=6\\Putting\ d=6\ in\ eqn\ 1\\40=a_1+6(6)\\40=a_1+36\\a_1=40-36\\a_1=4[/tex]
Putting the values of a1 and d in general form
[tex]a_n= a_1+(n-1)(6)\\a_n=4+6n-6\\a_n=6n-2\\Putting\ n=12\ \\a_{12}=6(12)-2\\=72-2\\=70[/tex]
The 12th term is 70
Answers:
Q1: a_n=2n+3
Q2: The 12th term of sequence is 70
Keywords: Arithmetic sequence, Common Difference
Learn more about arithmetic sequence at:
- brainly.com/question/4980053
- brainly.com/question/5002251
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