2 Answers

Ishan Fernando · Answer 1 · 2024-03-12T10:39:51+0000

The series -13, -7, -1, 5, 11 follows a pattern of adding 6 to each term successively. The representation that fits this progression is: -13 + 6K, where K denotes the term's position.

The given series is:

-13 + (-7) + (-1) + 5 + 11

This series forms a sequence by adding 6 to each consecutive term.

To represent this sequence in terms of an equation or expression, we can use a general formula:

$a_n = a_1 + (n - 1) \cdot d$

Where:

$a_n$ represents the nth term in the sequence.

$a_1$ is the first term.

$n$ is the term number.

$d$ is the common difference between terms.

For this series, the first term
$($a_1$)$ is -13, and the common difference
$($d$)$ is 6.

Let's find the 5th term in the sequence (as given series contains 5 terms):

$a_5 = a_1 + (5 - 1) \cdot d$

$a_5 = -13 + 4 \cdot 6$

$a_5 = -13 + 24$

$a_5 = 11$

The 5th term of the sequence is indeed 11, confirming that the pattern of adding 6 to each consecutive term holds true. Therefore, the correct representation corresponding to this series is: -13 + 6K, where
$K$ represents the position of the term in the sequence.

Bill Healey · Answer 2 · 2024-03-18T05:02:17+0000

The answer is
$\sum_(k=1)^(5)-13+6k$ . The last option is correct.

This is because we can see from the image that the series is arithmetic with a common difference of 6. The first term of the series is −13 and there are 5 terms in the series.

Therefore, the sum of the series is given by
$\sum_(k=1)^(5)-13+6k$

We can also see from the image that the series is equal to the sum of the following two series:

= -13+(-7)+(-1)+5+11 &= -13+(-7)+(-1)+(5+11)

= -13+(-7)+(-1)+16