Question

NO LINKS!! URGENT HELP PLEASE!!!

Write a rule for the nth term of this arithmetic sequence. Then find a_20.

3. 8, 21, 34, 47, 60, . . .

4. 6, 2, -2, -6, -10, . . .

Answer 1

3) an = 8 +13(n -1); a20 = 255

4) an = 6 -4(n -1); a20 = -70

Explanation:

You want the rule and the 20th term for the arithmetic sequences ...

3) 8, 21, 34, ...

4) 6, 2, -2, ...

Rule

The n-th term of an arithmetic sequence is given in terms of the first term (a1) and the common difference (d) as ...

an = a1 +d(n -1)

3.

The first term is 8. The common difference is 21 -8 = 13. The rule is ...

an = 8 +13(n -1)

The 20th term is ...

a20 = 8 +13(20 -1) = 255

4.

The first term is 6. The common difference is 2 -6 = -4. The rule is ...

an = 6 -4(n -1)

The 20th term is ...

a20 = 6 -4(20 -1) = -70

#95141404393

Answer 2

3. 255

4. -70

Explanation:

3.

For the arithmetic sequence 8, 21, 34, 47, 60, ...

The common difference between consecutive terms is d =(21-8)= 13. Therefore, the nth term of the sequence can be expressed as:

`\bold{a_n = a_1 + (n - 1) * d}`

where
`\bold{a_1}` is the first term of the sequence,

n is the term number, and d is the common difference.

Substituting
`a_1 = 8` and d = 13, we get:

`a_n = 8 + (n - 1) * 13\\a_n = 13n - 5`

To find
`a_(20)`, substitute n = 20 in the above formula:

`a_(20) = 13(20) - 5\\a_(20)= 255`

4.

For the arithmetic sequence 6, 2, -2, -6, -10, ...

The common difference between consecutive terms is d =(2-6)= -4. Therefore, the nth term of the sequence can be expressed as:

`\bold{a_n = a_1 + (n - 1) * d}`

where
`a_1` is the first term of the sequence,

n is the term number, and

d is a common difference.

Substituting
`a_1`= 6 and d = -4, we get:

`a_n = 6 + (n - 1) * (-4)\\a_n = 10 - 4n`

To find
`a_(20)`, substitute n = 20 in the above formula:

`a_(20) = 10 - 4(20)\\a_(20)= -70`