Answer :
Answer:
[tex]\boxed {a_{24} = 145}[/tex]
Step-by-step explanation:
According to the following pattern sequence ([tex]7, 13, 19, 25[/tex] ), it is Arithmetic Sequence, because every number is added by [tex]6[/tex]. So, to find the 24th term, you need to use the Arithmetic Sequence Formula and solve to find the 24th term:
[tex]a_{n} = a_{1} + (n - 1) d[/tex]
[tex]a_{n}[/tex]: nth term in the sequence
[tex]a_{1}[/tex]: 1st term
[tex]n[/tex]: term position
[tex]d[/tex]: Common difference
-Apply to the formula:
[tex]a_{24} = 7 + 6 (24 - 1)[/tex]
[tex]a_{n} = a_{24}[/tex]
[tex]a_{1} = 7[/tex]
[tex]n = 24[/tex]
[tex]d = 6[/tex]
-Solve:
[tex]a_{24} = 7 + 6 (24 - 1)[/tex]
[tex]a_{24} = 7 + 6 (23)[/tex]
[tex]a_{24} = 7 + 138[/tex]
[tex]\boxed {a_{24} = 145}[/tex]
Therefore, the 24th term is [tex]145[/tex].
The 24th term of the sequence is 145
7, 13 , 19, 25
The sequence is an arithmetic progression. Therefore, let's use arithmetic progression formula for nth term to find the 24th term.
Arithmetic progression:
- aₙ = a + (n - 1)d
where
a = first term
d = common difference
n = number of term
Therefore,
d = 13 - 7 = 6
a = 7
a₂₄ = 7 + (24 - 1)6
a₂₄ = 7 + (23)6
a₂₄ = 7 + 138
a₂₄ = 145
Therefore, the 24th term of the sequence is 145
learn more on sequence here: https://brainly.com/question/14092689