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The next number in the arithmetic sequence [tex]70, 54, 38, \ldots[/tex] is:

A. 24
B. 20
C. 30
D. 22
E. 26

Sagot :

GinnyAnsweridn
To find the next number in the arithmetic sequence [tex]\( 70, 54, 38 \)[/tex], we need to follow these steps:

1. Identify the sequence: The given sequence is [tex]\( 70, 54, 38 \)[/tex].

2. Determine the common difference:
- Subtract the second term from the first term: [tex]\( 54 - 70 = -16 \)[/tex].
- Validate this by subtracting the third term from the second term: [tex]\( 38 - 54 = -16 \)[/tex].
- Hence, the common difference [tex]\( d \)[/tex] is [tex]\(-16\)[/tex].

3. Calculate the next term:
- The next term in the sequence can be found by adding the common difference to the last term in the sequence.
- The last term given is 38, so the next term will be: [tex]\( 38 + (-16) = 38 - 16 = 22 \)[/tex].

Thus, the next number in the arithmetic sequence is
[tex]\[ 22 \][/tex].

So the correct answer is [tex]\[ 22 \][/tex].
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