A row in Pascals triangle starts as follows 1 16 120 560 182

A row in Pascal’s triangle starts as follows:

1 16 120 560 1820 4368 ...

Find the next term in this row. Find the first five terms in the next row of Pascal’s triangle.

Solution

The 2nd term in the row says the row number.

Thus, this must be filled with terms of 16Cn.

Thus, the next term here is 16C6 = 8008 [ANSWER]

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The next row is composed of terms 17Cn. Thus, the first 5 terms are

17C0 = 1
17C1 = 17
17C2 = 136
17C3 =680
17C4 =2380 [ANSWERS]