the difference between two terms of the sequence A is 4 (7-3=11-7=...=4) and the difference between two terms of the sequence B is 7 (9-2=16-9=...-7). It means, in the final sequence the difference should be 7*4=28;

2. to calculate the first term of the final sequence:

A={3;7;11;15;19;<u>23</u>;27;31;...;407} and B{2;9;16;<u>23</u>;30;...;709}. It means, the first term of the final sequence is 23.

3. to calculate the last term of the final sequence:

if 407<709, it means the last term is less than 407, then it is possible to make up the equation 23+28*n<407, where 23 - the 1st term of the final sequence, 28 - the difference of the final sequence, (n+1) - number of the last term of the final sequence and n∈Z.

n<(407-23)/28; n<13.71. If n∈Z, then n=13.

So, the last term of the final sequence is 23+28*13=387.

4. if the first term is 23, the last one is 387 and the difference of the final sequence is 28, then the final sequence is consists of 14 terms:

{23; 51; 79; 107; 135; 163; 191; 219; 247; 275; 303; 331; 359; 387}

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3 years ago