Answer:
[tex]a_{24}=146[/tex]
Step-by-step explanation:
The formula of a nth term of n arithmetic sequence:
[tex]a_n=a_1+(n-1)d[/tex]
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[tex]a_m=a_1+(m-1)d\\\\a_m-a_n=(a_1+(m-1)d)-(a_1+(n-1)d)\\\\=a_1+(m-1)d-a_1-(n-1)d=(m-1)d-(n-1)d=(m-1-n+1)d=(m-n)d[/tex]
Therefore
[tex]a_9-a_1=(9-1)d=8d[/tex]
[tex]8d=56-8\\8d=48\qquad|:8\\d=6[/tex]
Substitute:
[tex]a_1=8,\ d=6,\ n=24\\\\a_{24}=8+(24-1)(6)=8+(23)(6)=8+138=146[/tex]
