Answer:
A) 1, 4, 7, 11, . . .
B) aₙ = aₙ₋₁ + 3
C) T₁₅ = 43
Step-by-step explanation:
A) From the graph, we see the points are: [tex]$ (1,1), (2,4), (3,7) $[/tex].
This means [tex]$ a = 1 $[/tex]
[tex]$ a_2 = a + d = 4 $[/tex]
[tex]$a_3 = a + 2d = 7 $[/tex]
The general term of the arithmetic sequence is: [tex]$ a, a+d, a+2d, a+3d, . . . $[/tex] where, [tex]$ a$[/tex] is the first term;
[tex]$ a + d $[/tex] is the second term and
[tex]$ d $[/tex] is the common difference.
Here, we see that the first term is 1. Second term is 4. Third term is 7. That means each consecutive term is obtained by adding 3 to the previous term. Therefore, according to our assumptions, common difference, [tex]$ d = 3 $[/tex].
B) Recursive formula represents the general form of an arithmetic sequence.
Here, since, [tex]$ n^{th} $[/tex] term is obtained by adding 3 to the previous term, the recursive formula would be: [tex]$ a_n = a_{n - 1} + 3 $[/tex].
C) [tex]$ 15^{th} $[/tex] term:
The formula to calculate [tex]$ n^{th} $[/tex] term is: [tex]$ T_n = a + (n - 1)d $[/tex].
Therefore, to find the [tex]$ 15^{th} $[/tex] term, we would have:
[tex]$ T_{15} = 1 + (15 - 1)(3) $[/tex]
[tex]$ =1 + 14(3) $[/tex]
[tex]$ \therefore, T_{15} = 43 $[/tex]
