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
