Question

Write a statement that correctly describes the relationship between these two sequences: 2, 4, 6, 8, 10 and 1, 2, 3, 4, 5.0.

Answer 1

`S_(a)` = 2
`S_(b)`

where:
`S_(a)` is the sum of the terms in the first sequence, and
`S_(b)` is the sum of the terms in the second sequence.

Explanation:

The two sequences are arithmetic progression.

From the first sequence,

first term, a = 2

common difference, d = 2

number of terms, n = 5

From the second sequence,

first term, a = 1

common difference, d = 1

number of terms, n = 5

The sum of terms of an arithmetic progression is given as;

=
`(n)/(2)`[2a + (n - 1) x d]

⇒ Let the sum of the first sequence be represented by
`S_(a)`, so that;

`S_(a)` =
`(5)/(2)`[2(2) + (5 - 1) x 2]

=
`(5)/(2)`[4 + 8]

=
`(5)/(2)` x 12

`S_(a)` = 30

⇒ Let the sum of the second sequence be represented by
`S_(b)`, so that;

`S_(b)` =
`(5)/(2)`[2(1) + (5 - 1) x 1]

=
`(5)/(2)`[2 + 4]

`S_(b)` = 15

Thus, the statement that would correctly describe the relationship between the sequences is;

`S_(a)` = 2
`S_(b)`

where:
`S_(a)` is the sum of the terms in the first sequence, and
`S_(b)` is the sum of the terms in the second sequence.