Answer:
[tex]S_{a}[/tex] = 2[tex]S_{b}[/tex]
where: [tex]S_{a}[/tex] is the sum of the terms in the first sequence, and [tex]S_{b}[/tex] is the sum of the terms in the second sequence.
Step-by-step 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;
= [tex]\frac{n}{2}[/tex][2a + (n - 1) x d]
⇒ Let the sum of the first sequence be represented by [tex]S_{a}[/tex], so that;
[tex]S_{a}[/tex] = [tex]\frac{5}{2}[/tex][2(2) + (5 - 1) x 2]
= [tex]\frac{5}{2}[/tex][4 + 8]
= [tex]\frac{5}{2}[/tex] x 12
[tex]S_{a}[/tex] = 30
⇒ Let the sum of the second sequence be represented by [tex]S_{b}[/tex], so that;
[tex]S_{b}[/tex] = [tex]\frac{5}{2}[/tex][2(1) + (5 - 1) x 1]
= [tex]\frac{5}{2}[/tex][2 + 4]
[tex]S_{b}[/tex] = 15
Thus, the statement that would correctly describe the relationship between the sequences is;
[tex]S_{a}[/tex] = 2[tex]S_{b}[/tex]
where: [tex]S_{a}[/tex] is the sum of the terms in the first sequence, and [tex]S_{b}[/tex] is the sum of the terms in the second sequence.
