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Answer :
The value of the 24th term in the given arithmetic sequence is 152.
To find the value of the 24th term in the given arithmetic sequence, we first need to determine the common difference d between consecutive terms.
The common difference is calculated by subtracting any term from its succeeding term. For instance:
[tex]\[ -2 - (-9) = 7 \][/tex]
[tex]\[ 5 - (-2) = 7 \][/tex]
[tex]\[ 12 - 5 = 7 \][/tex]
This shows that the common difference d is 7.
Now, to find the value of the 24th term, we use the formula for the nth term of an arithmetic sequence:
[tex]\[ a_n = a_1 + (n-1) \cdot d \][/tex]
We are given:
[tex]\( a_1 = -9 \),[/tex]
[tex]\( d = 7 \)[/tex], and
[tex]\( n = 24 \).[/tex]
Substituting these values into the formula:
[tex]\[ a_{24} = -9 + (24-1) \cdot 7 \][/tex]
[tex]\[ a_{24} = -9 + 23 \cdot 7 \][/tex]
[tex]\[ a_{24} = -9 + 161 \][/tex]
[tex]\[ a_{24} = 152 \][/tex]
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Answer:
152
Step-by-step explanation:
this is an arithmetic sequence, since the gap between values is the same (-2 - -9 = 7, 5 - -2 = 7......)
the first value, a, is -9. the common difference is 7. n is position in sequence.
formula for arithmetic sequence = a + (n-1)d
= -9 + (n-1) 7
= -9 + 7n -7
=7n -16.
so the 24th term is 7(24) - 16
= 152.
