Help with algebra please?

Question

I need some help with algebra I'm not sure how to get to the answer.

Find the number of terms in each sequence.

1. a1=4 an=42 d=2

2. a1--0.3 an=-36 d=2.1

3. 1/12, 1/8, 1/6, 5/24, 1/4,......9/8

Evaluate each sum.

1. There is an e like symbol that has a 15 on top on the bottom n=4 and to the right (3-5n)

Answer 1

1.

The first term of the sequence a1 = 4 ,

The common term d = 2

The nth term  an = a + (n - 1)d = 42

Substitute a1 = 4 and d = 2 then

4 + (n - 1)2 = 42

Subtract 4 to each side

(n - 1)2 = 38

Divide each side by 2

n - 1 = 19

Add 1 to each side

n = 19 + 1

n = 20

Therefore the number of terms in the sequence : 20.

 

Answer 2

2.

The first term of the sequence a1 = -0.3 ,

The common term d = -2.1

The nth term  an = a + (n - 1)d = -36

Substitute a1 = -0.3 and d = -2.1 then

-0.3 + (n - 1)-2.1 = -36

Add 0.3 to each side

(n - 1)-2.1 = -35.7

Divide each side by negitive 2.1

n - 1 = 17

Add 1 to each side

n = 17 + 1

n = 18

Therefore the number of terms in the sequence : 18.

 

Answer 3

3.

The first term of the sequence a1 = 1 / 12 ,

The common term d = 1 / 8 - 1 / 12 = 3 / 24 - 2 / 24 = 1 / 24

The nth term  an = a + (n - 1)d = 9 / 8

Substitute a1 = 1 / 12 and d = 1 / 24 then

1 / 12 + (n - 1)1 / 24 = 9 / 8

Subtract 1 / 12 from each side

(n - 1)1 / 24 = 9 / 8 - 1 / 12 = 25 / 24

Multiply each side by 24

n - 1 = 25

Add 1 to each side

n = 25 + 1

n = 26

Therefore the number of terms in the sequence : 26.

Answer 4

The first term of the sequence a1 = 4 ,

The common term d = 2

The nth term  an = a + (n - 1)d = 42

Substitute a1 = 4 and d = 2 then

4 + (n - 1)2 = 42

Subtract 4 to each side

(n - 1)2 = 38

Divide each side by 2

n - 1 = 19

Add 1 to each side

n = 19 + 1

n = 20

Therefore the number of terms in the sequence : 20

The sum of the sequence formula = n / 2[2a1 + (n - 1)d]

Substitute a1 = 4 , d = 2 and n = 20 then

20 / 2[2(4) + (20 - 1) 2]

10[8 + 38]

10[46]

460.

Answer 5

The first term of the sequence a1 = -0.3 ,

The common term d = -2.1

The nth term  an = a1 + (n - 1)d = -36

Substitute a1 = -0.3 and d = -2.1 then

-0.3 + (n - 1)-2.1 = -36

Add 0.3 to each side

(n - 1)-2.1 = -35.7

Divide each side by negitive 2.1

n - 1 = 17

Add 1 to each side

n = 17 + 1

n = 18

Therefore the number of terms in the sequence : 18

The sum of the sequence formula = n / 2[2a1 + (n - 1)d]

Substitute a1 = -0.3 , d = -2.1 and n = 18 then

18 / 2[2(-0.3) + (18 - 1) -2.1]

9[-0.6 + -35.7]

9[-36.3]

-326.70.

Answer 6

The first term of the sequence a1 = 1 / 12 ,

The common term d = 1 / 24

The nth term  an = a1 + (n - 1)d = 9 / 8

Substitute a1 = 1 / 12 and d = 1 / 24 then

1 / 24 + (n - 1)1 / 24 = 9 / 8

Subtract 1 / 24 from each side

(n - 1)1 / 24 = 27 / 24 - 2 / 24

Multiply each side by 24

n - 1 = 25

Add 1 to each side

n = 25 + 1

n = 26

Therefore the number of terms in the sequence : 26

The sum of the sequence formula = n / 2[2a1 + (n - 1)d]

Substitute a1 = 1 / 12 , d = 1 / 24 and n = 26 then

26 / 2[2(1 / 24) + (26 - 1) 1 / 24]

13[2 / 24 + 25 / 24]

13[27 / 24]

351 / 24

The sum of the sequence : 351 / 24.

Comments

Sum of the sequence

Substitute a1 = 1/12 , d = 1/24 and n = 26 then in