Answer:
a₈ = 37
Step-by-step explanation:
The given arithmetic sequence is: 3, 8, 13, 18, 23, . . .
The recursive formula for the sequence is: [tex]$ a_n = a_{n - 1} + 5 $[/tex]
Here, [tex]$ a_n $[/tex] represents the [tex]$ n^{th} $[/tex] of the sequence.
And, [tex]$ a_{n - 1} $[/tex] represents the [tex]$ (n - 1)^{th} $[/tex] of the sequence.
'+5' denotes that '5' is added to the [tex]$ (n - 1)^{th} $[/tex] term to get the [tex]$ n^{th} $[/tex] term. In other words, the difference between two consecutive numbers in the sequence is 5.
Now, we are asked to find a₈ i.e., n =8.
Substituting in the recursive formula we get: a₈ = a₍₈₋ ₁₎ + 5 = a₇ + 5.
So, to determine a₈ we need to know a₇. From the sequence we see that a₅ = 23.
⇒ a₆ = 23 + 5 = 28.
⇒ a₇ = 28 + 5 = 32.
⇒ a₈ = 32 + 5 = 37.
Therefore, the [tex]$ 8^{th} $[/tex] term of the sequence is 37.
