Question

Could someone please help me with this? I would mark you as Brainliest:)

Answer 1

Answer:

a) The table of values represents the ordered pairs formed by the elements of the sequence ($a_{i}$) (range) and their respective indexes ($i$) (domain):

$i$         $a_{i}$

1         6

2        11

3        16

4        21

5        26

b) The algebraic expression for the general term of the sequence is $a(i) = 6 + 5\cdot (i - 1)$.

c) The 25th term in the sequence is 126.

Step-by-step explanation:

a) Make a table of values for the sequence 6, 11, 16, 21, 26, ...

The table of values represents the ordered pairs formed by the elements of the sequence ($a_{i}$) (range) and their respective indexes ($i$) (domain):

$i$         $a_{i}$

1         6

2        11

3        16

4        21

5        26

b) Based on the table of values, we notice a constant difference between two consecutive elements of the sequence, a characteristic of arithmetic series, whose form is:

$a(i) = a_{1} + r\cdot (i - 1)$ (1)

Where:

$a_{1}$ - First element of the sequence.

$r$ - Arithmetic difference.

$i$ - Index.

If we know that $a_{1} = 6$ and $r = 5$, then the algebraic expression for the general term of the sequence is:

$a(i) = 6 + 5\cdot (i - 1)$

c) If we know that $a(i) = 6 + 5\cdot (i - 1)$ and $i = 25$, then the 25th term in the sequence is:

$a(25) = 6 + 5\cdot (25 - 1)$

$a(25) = 126$

The 25th term in the sequence is 126.