Question

find the next term in the sequence 3,13/4,7/2,15/4,__?​

Answer 1

Answer:

Arithmetic Sequence:

The common difference in the arithmetic sequence 3, 13/4, 7/2, 15/4 is ¼. To find the difference, use the formula: d = a₂ – a₁. An arithmetic sequence is a sequence of numbers such that the difference of any two consecutive terms of the sequence is a constant. While an arithmetic series is the sum of the terms of the arithmetic sequence.

Definition of arithmetic sequence: brainly.ph/question/554855

Examples of arithmetic sequence: brainly.ph/question/608143

Solution:

1. Given the following:

a₁ = 3

a₂ = 13/4

a₃ = 7/2

a₄ = 15/4

2. Find the difference between the second term and the first term.

d = a₂ – a₁

d = 13/4 – 3

d = 13/4 – 3(4)/4

d = 13/4 – 12/4

d = ¼

3. Therefore, the common difference is ¼.

Other Examples:

Find the common difference of the arithmetic sequence 4, −1, −6, −11, …

Solution:

1. Given:

a₁ = 4

a₂ = -1

a₃ = -6

a₄ = -11

Find the common difference.

d = a₂ – a₁

d = -1 – 4

d = -5

Therefore, the common difference of the arithmetic sequence 4, −1, −6, −11, … is -5.

Find the common difference of the arithmetic sequence -3, 1, 5, 9, 13...

Solution:

Given:

a₁ = -3

a₂ = 1

a₃ = 5

a₄ = 9

a₅ = 13

Use d = a₂ - a₁

d = 1 - (-3)

d = 1 + 3

d = 4

Therefore, the common difference of the arithmetic sequence 3, 1, 5, 9, 13... is 4.

Step-by-step explanation:

hope it helps

Answer 2

4 is the next term of the series.

Given:

$3, \frac{13}{4}, \frac{7}{2},\frac{15}{4}$

To find:

We have to find the next term in the sequence.

Solution:

we can see a pattern in the whole sequence.

The difference between the proceeding term and the previous term is the difference of $\frac{1}{4}$

for example:

$=\frac{13}{4} - 3\\\\=\frac{13-12}{4}\\\\= \frac{1}{4}$

Similarly, we can do this for other terms as well

$\frac{7}{2} - \frac{13}{4} \\\\= \frac{14-13}{4}\\\\= \frac{1}{4}$

Hence, for the next term of the series

$=\frac{15}{4} + \frac{1}{4}\\\\=\frac{16}{4}\\\\= 4$

Therefore 4 is the next term of the series.