7; p; -3;q;...
Given the first four terms of a linear pattern : 1. Calculate the values of p and q
A quadratic sequence is defined as 2; 12; 28; 50
2. Write down the next two terms Determine the nth term in the form T₁ = ..
3. Calculate T40 of this sequence.
4. Calculate the first difference between T₁ and Tn-1 where T₁= 688
The n-th term of a number pattern is as follows: Tn = 7n + 6 if n is a prime number and T₁ = n²-8 if n is not prime number
6. Determine the value of T, - T7

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ayoushivt ayoushivt · Answer 1 · 2022-06-23T11:01:46+02:00

The value of p and q is 2 , -8 , The nth term of the series is given by 3 * n² + n-2 , the 40th term is 4838 .

A sequence which has n term in its sequence , The difference of the consecutive number is not same , its second difference is same.

The sequence is given as 7; p; -3;q;...

for a linear pattern

7-p = p- (-3) = -3-q

2p = 4

p = 2

and

2+3 = -3 -q

5 +3 = -q

q = -8

The value of p and q is 2 , -8

A quadratic sequence is defined as 2; 12; 28; 50

The next two terms are 77 and 112.

3. The T40 of the sequence is

The nth term of the series is given by

3 * n² + n-2

therefore 40th term is

3 *40² + 40-2

3 *1600 +38

4838

Therefore the 40th term is 4838 .

To know more about Quadratic Sequence

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