Answer:
x=15
Explanation:
The pattern of numbers can be re-written in the form below:
![\left\begin{array}{ccccccccccccc}&&&&&&1&&&\\&&&&&1& &1&&&\\&&&&1& &2 &&1\\&&&1 &&3 &&3 &&1\\ &&1 &&4 &&6&& 4&& 1\\ &1 &&5&&10&&10&&5&&1\\ 1 &&6 &&x &&20&& x &&6 &&1\end{array}\right \\]()
The triangular array which involves summing adjacent elements in preceding rows is referred to as the Paschal's Triangle.
Taking the 6th and seventh row, the adjacent elements in the 6th row are summed on the Left Hand sides and the result from the seventh row is given on the right hand sides of the equations below.
- 1+5=6
- 5+10=x
- 10+10=20
- 10+5=x
- 5+1=6
We can then see that:
5+10=x; and
10+5=x
10+5=5+10=15
Therefore:
x=15