Question

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

14, 21, 42, 77, ...

yes; 7
yes; –7
yes; 14
no
6. What is the 12th term of the sequence 10, 6, 2, …?
–16
–24
–34
–38
7. Find the missing term of the arithmetic sequence 22, ___ , 34, ...
46
16
28
40

Answer 1

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.

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.

Answer 2

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