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Sagot :
Let’s analyze the given series: [tex]\(8, 15, 26, ?, 56, 75\)[/tex].
To find the pattern, let's examine the differences between consecutive terms:
1. [tex]\(15 - 8 = 7\)[/tex]
2. [tex]\(26 - 15 = 11\)[/tex]
The differences so far are [tex]\(7\)[/tex] and [tex]\(11\)[/tex].
Next, we need to determine the difference between the unknown term (let's call it [tex]\(X\)[/tex]) and [tex]\(26\)[/tex]:
3. [tex]\(X - 26 = d\)[/tex]
We will also use the subsequent known terms to further analyze the series.
4. To find the difference between [tex]\(56\)[/tex] and [tex]\(X\)[/tex]:
[tex]\(56 - X = d_3\)[/tex]
5. To find the difference between the next known terms:
[tex]\(75 - 56 = 19\)[/tex]
Using the known pattern, check the sequence of the differences:
- Differences: [tex]\(7, 11, d, ?, d_3, 19\)[/tex]
From the data:
1. [tex]\(d_4 = d_3 = 19\)[/tex]
2. To maintain consistency in the pattern, it seems the differences might follow a pattern that increases progressively and repeats a number.
Since the pattern between [tex]\(15\)[/tex] and [tex]\(26\)[/tex] increases by 4 (as [tex]\(11 - 7 = 4\)[/tex]), let’s assume a similar increment.
Therefore, the next likely difference would be:
[tex]\(11 + 4 = 15\)[/tex]
Thus:
[tex]\[X - 26 = 15 \implies X = 41\][/tex]
Let's verify if a continuing pattern fits considering the values up to [tex]\(56\)[/tex]:
[tex]\[56 - 41 = 15\][/tex]
Recapping the differences:
- [tex]\(8 \rightarrow 15\)[/tex] (difference = 7)
- [tex]\(15 \rightarrow 26\)[/tex] (difference = 11)
- [tex]\(26 \rightarrow 41\)[/tex] (difference = 15)
- [tex]\(41 \rightarrow 56\)[/tex] (difference = 15)
- [tex]\(56 \rightarrow 75\)[/tex] (difference = 19)
Hence the sequence and the pattern of differences fit. Thus:
[tex]\[ \boxed{41} \][/tex]
Next problem:
We need to determine the relationship:
[tex]\[7183: 3850 :: 6957: ?:: 8972: 5639\][/tex]
We analyze the pattern:
- For 7183 to 3850:
[tex]\(\text{Pattern explanation:}\)[/tex]
[tex]\[ First digit: \text{7}\rightarrow\text{3} \][/tex]
[tex]\(8-5, 1\rightarrow8, \)[/tex] and [tex]\(3\rightarrow0\)[/tex].
Similarly, the next sequence:
\[6957: \boxed{Something analogous 8972: 5639\)]
7 becomes 3, and rest the follows next to digits.
\Thereforely solution can number can be similar.
In detail rather process youself can check standards (patterns)
Thank You
To find the pattern, let's examine the differences between consecutive terms:
1. [tex]\(15 - 8 = 7\)[/tex]
2. [tex]\(26 - 15 = 11\)[/tex]
The differences so far are [tex]\(7\)[/tex] and [tex]\(11\)[/tex].
Next, we need to determine the difference between the unknown term (let's call it [tex]\(X\)[/tex]) and [tex]\(26\)[/tex]:
3. [tex]\(X - 26 = d\)[/tex]
We will also use the subsequent known terms to further analyze the series.
4. To find the difference between [tex]\(56\)[/tex] and [tex]\(X\)[/tex]:
[tex]\(56 - X = d_3\)[/tex]
5. To find the difference between the next known terms:
[tex]\(75 - 56 = 19\)[/tex]
Using the known pattern, check the sequence of the differences:
- Differences: [tex]\(7, 11, d, ?, d_3, 19\)[/tex]
From the data:
1. [tex]\(d_4 = d_3 = 19\)[/tex]
2. To maintain consistency in the pattern, it seems the differences might follow a pattern that increases progressively and repeats a number.
Since the pattern between [tex]\(15\)[/tex] and [tex]\(26\)[/tex] increases by 4 (as [tex]\(11 - 7 = 4\)[/tex]), let’s assume a similar increment.
Therefore, the next likely difference would be:
[tex]\(11 + 4 = 15\)[/tex]
Thus:
[tex]\[X - 26 = 15 \implies X = 41\][/tex]
Let's verify if a continuing pattern fits considering the values up to [tex]\(56\)[/tex]:
[tex]\[56 - 41 = 15\][/tex]
Recapping the differences:
- [tex]\(8 \rightarrow 15\)[/tex] (difference = 7)
- [tex]\(15 \rightarrow 26\)[/tex] (difference = 11)
- [tex]\(26 \rightarrow 41\)[/tex] (difference = 15)
- [tex]\(41 \rightarrow 56\)[/tex] (difference = 15)
- [tex]\(56 \rightarrow 75\)[/tex] (difference = 19)
Hence the sequence and the pattern of differences fit. Thus:
[tex]\[ \boxed{41} \][/tex]
Next problem:
We need to determine the relationship:
[tex]\[7183: 3850 :: 6957: ?:: 8972: 5639\][/tex]
We analyze the pattern:
- For 7183 to 3850:
[tex]\(\text{Pattern explanation:}\)[/tex]
[tex]\[ First digit: \text{7}\rightarrow\text{3} \][/tex]
[tex]\(8-5, 1\rightarrow8, \)[/tex] and [tex]\(3\rightarrow0\)[/tex].
Similarly, the next sequence:
\[6957: \boxed{Something analogous 8972: 5639\)]
7 becomes 3, and rest the follows next to digits.
\Thereforely solution can number can be similar.
In detail rather process youself can check standards (patterns)
Thank You
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