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  1. Is the sequence arithmetic? If so, identify the common difference.

14, 21, 42, 77, ...


yes; 7

yes; –7

yes; 14

no

  1. What is the 12th term of the sequence 10, 6, 2, …?

–16

–24

–34

–38

  1. Find the missing term of the arithmetic sequence 22, ___ , 34, ...

46

16

28

40

Verified Answer :

apologiabiology

5.
aritmetic is same increase per term
14 to 21 is 7
21 to 42 is 21
7≠21
no


6.
decreases by 4 each time
an=a1+d(n-1)
an=10-4(n-1)
n=12 for 12th term
a12=10-4(12-1)
a12=10-4(11)
a12=10-44
a12=-34

it is -34



7.
missing term is y
22+n=y
y+n=34
22+n+n=34
22+2n=34
minus 22 from both sides
2n=12
divide both sides by 2
n=6
22+n=y
22+6=y
28=y

28 is answer



5. no
6. -34
7. 28

Answer:

5. The correct option is 4. No, the given sequence is not arithmetic.

6.The option 3 is correct and the 12th term of the sequence is -34.

7. The option 3 is correct and the missing term of the arithmetic sequence is 28.

Step-by-step explanation:

5.

The given sequence is

\(14,21,42,77\)

\(d_1=a_2-a_1=21-14=7\)

\(d_2=a_3-a_2=42-21=21\)

Since \(d_1 eq d_2\), therefore it is not an arithmetic sequence. Option 4 is correct.

6.

The given sequence is

\(10,6,2,...\)

First term is 10 and common difference is -4.

The formula for nth term is

\(a_n=a+(n-1)d\)

\(a_{12}=10+({12}-1)(-4)=10-44=-34\)

Therefore option 3 is correct and the 12th term of the sequence is -34.

7.

The given sequence is

22, ___ , 34, ...

In an arithmetic sequence

\(2b=a+c\)

\(2b=22+34\)

\(2b=56\)

\(b=28\)

Therefore option 3 is correct and the missing term of the arithmetic sequence is 28.

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