Answer:
The rule of the arithmetic sequence is 13 - 2n
The 30th term is -47
Step-by-step explanation:
∵ f(n) = 11 and g(n) = -2(n - 1) = -2n + 2
∴ f(n) + g(n) = 11 + -2n + 2 = 13 - 2n
Use n = 1 , 2 , 3 , 4 to check the type of the sequence
∵ n = 1 ⇒ 13 - 2(1) = 11
∵ n = 2 ⇒ 13 - 2(2) = 13 - 4 = 9
∵ n = 3 ⇒ 13 - 2(3) = 13 - 6 = 7
∵ n = 4 ⇒ 13 - 2(4) = 13 - 8 = 5
∵ 11 , 9 , 7 , 5 is an arithmetic sequence with difference -2
∴ The rule of the arithmetic sequence is 13 - 2n
∴ The 30th term = 13 - 2(30) = -47
Answer:
The formula for arithmetic sequence is 13-2n.the the 30th term of arithmetic sequence is -47.
Step-by-step explanation:
We have given two functions:
f(n) = 11 , g(n) = −2(n − 1)
We combine them to create an arithmetic sequence.
f(n)+g(n) = 11 +(-2(n-1))
f(n)+g(n) = 11 + (-2n+2)
f(n)+g(n) = 11 -2n+2
f(n)+g(n) = 13 - 2n
Put n = 1,2,3,4,......... for checking the type of sequence.
For n=1
13-2(1)=11
For n = 2
13-2(2) =9
For n = 3
13- 2(3) = 7
The difference between terms are -2.
It is the arithmetic sequence.
The formula of arithmetic sequence is 13-2n.
the the 30th term of arithmetic sequence is :
put n = 30
13-2(30) = 13 -60 = -47
The the 30th term of arithmetic sequence is -47.
