Answer:
[tex]a_{24} = 146[/tex]
Step-by-step explanation:
a1 = 8
a9 = 56
Using formula for finding nth term of arithmeric sequence
[tex]a_{n} =a_{1} + (n-1)d[/tex]
We have to find 24th term, therefore n = 24
[tex] a_{1}[/tex] is the first term but we are missing d
d is the difference between the two consecutive terms, lets calculate it first
a9 = 56
Using the above given formula for finding d
put n = 9, a9= 56
[tex]a_{9} =a_{1}+ (9-1)d[/tex]
56 = 8 + 8d
8d = 48
d = 6
Getting back to main part of finding 24th term
n = 24, d = 6, a1 = 8
put values in nth term formula
[tex]a_{n} =a_{1}+ (n-1)d[/tex]
[tex]a_{24} = 8 + (24-1)6[/tex]
[tex]a_{24} = 8 + 138[/tex]
[tex]a_{24} = 146[/tex]
