Question
1.4 A quadratic pattern has a second term equal to 1 and a third term equal to -6 and a
fifth term equal to -14 .
1.4 .1 calculate the second differences of this quadratic pattern
1.4 .2 hence, or otherwise, calculate the first term of the pattern
1.5
fifth term equal to -14 .
1.4 .1 calculate the second differences of this quadratic pattern
1.4 .2 hence, or otherwise, calculate the first term of the pattern
1.5
Ask by Fernandez Campbell. in South Africa
Jan 16,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
1.4 Quadratic Pattern
- Second Differences: Calculated to be 1.
- First Term: 10.
1.5 Quadratic Pattern
- Value of
: 20. - General Term:
.
1.6 Sequence with Constant Second Difference
- Values of
and : -
Solution

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Mind Expander
To dive into the world of quadratic patterns, let’s start with the basics! For any quadratic sequence like the one you specified, the second differences are found by taking the differences of the first differences. Since you’re given the second and third terms, you can find the first differences and then calculate the second differences. In this case, with a consistent second difference, this reveals the underlying quadratic nature behind the numbers!
Now, onto finding the missing terms! Once you’ve established the second difference (which must be constant for a quadratic sequence), you can use it to work backward to determine earlier terms. Having found the second differences allows you to create a system of equations with known values to uncover the first and subsequent missing terms, offering a logical pathway to determine the complete pattern! Keep calculating and enjoy the logical journey of quadratic sequences!