Question

I need help with this please

Answer 1

`\sf\\\textsf{Here, the number of small triangles in 1st triangle= 1}\\\textsf{Number of small triangles in 2nd triangle = 2}\\\textsf{Number of small triangles in 3rd triangle = 9}\\`

`\sf\\\textsf{This can be written in sequence as:}\\1,4,9,...\\\textsf{or, }1^2, 2^2,3^2,...\\\\\textsf{Now these are the sequence of squares of natural numbers. Natural numbers are}\\\textsf{the numbers used for counting, such as 1, 2, 3,...}`

`\sf\\\textsf{This means the nth term of the sequence will be }n^2\textsf{ where, 'n' is the number of }\\\textsf{small triangles in the nth figure.}`

`\textsf{This means, all you have to do is simply replace 100 with n, to find the number of}\\\textsf{small triangles the 100th figure would contain.}`