Question

Help me :,)

Answer 1

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 2

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.