Question

Make an algebraic expression to determine the 15th term of this pattern:

63, (63+23), (63+23+30), (63+23+30+37), ...

And please, give me a complete answer with a step-by-step explanation.

Answer 1

63+23+30+37+44+51+58+65+72+79+86+93+100+107+114.

Explanation:

1. according to the condition 63+23; 63+23+30; 63+23+30+37+...; is an arithmetic sequence (note, 63 does not belong to it);

2. according to the condition the 1st term is 63+23; the 2d term is 63+23+30; the 3d term is 63+23+30+37, etc. It means, the next term is calculated with '+7';

3. according to the item '1.' the number '63' was excluded from the initial pattern. It means, the 14th term should be calculated: 23+7*(14-1)=114.

4. if number '63' is included into the given pattern again, the 15th term of the given pattern is 63+0+23+30+...+98.

5. the 15th term is:

63+23+30+37+44+51+58+65+72+79+86+93+100+107+114.