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Insertion of AP's between 2 Numbers

7, 10, 15, ,3...

Question

7, 10, 15, ,31., 42, 55, _, 87

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Solution

Loot carefully at above sequence Take the 1st difference of each consecutive term
7, 10, 15, , 31, 42, 55, _, 87
3, 5, _, _, 11, 13, _, _
Does this first difference sequence now look familiar ? this is an arithmetic progression just as we saw in the first question
3, 5, 7, 9, 11, 13, 15, 17
In this case the difference are in arithmetic progression
Therefore the series is 7,10,15,22,32,42,55,70,87.

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