It is a superstition of mathematically illiterate people to believe

    that such questions "what number is next" make sense.


    Actually, they do not.


    Same as to believe that the Earth is flat.


    It is with GREAT SORROW I observe that Edwin supports this superstition at this forum.

The pattern consists of these 5 steps: 

1. Multiply the number of term by 3.
2. Subtract from 25.
3. Multiply by the number of term.
4. Double.
5. Add 25.

So to get term number 1:

1. Multiply the number of term by 3, 1×3 = 3.
2. Subtract from 25, get 25-3 = 22.
3. Multiply by the number of term, get 22×1 = 22.
4. Double, get 2×22 = 44.
5. Add 25, get 44+25 = 69, which checks.

To get term number 2:

1. Multiply the number of term by 3, 2×3 = 6.
2. Subtract from 25, get 25-6 = 19.
3. Multiply by the number of term, get 19×2 = 38.
4. Double, get 2×38 = 76.
5. Add 25, get 76+25 = 101, which checks.

To get term number 3:

1. Multiply the number of term by 3, 3×3 = 9.
2. Subtract from 25, get 25-9 = 16.
3. Multiply by the number of term, get 16×3 = 48.
4. Double, get 2×48 = 96.
5. Add 25, get 96+25 = 121, which checks.

So we have the right pattern.

To get term number 4:

1. Multiply the number of term by 3, 4×3 = 12.
2. Subtract from 25, get 25-12 = 13.
3. Multiply by the number of term, get 13×4 = 52.
4. Double, get 2×52 = 104.
5. Add 25, get 104+25 = 129.

To get term number 5:

1. Multiply the number of term by 3, 5×3 = 15.
2. Subtract from 25, get 25-15 = 10.
3. Multiply by the number of term, get 10×5 = 50.
4. Double, get 2×50 = 100.
5. Add 25, get 100+25 = 125.

Answer: 129 and 125 are the next two terms.

Edwin