Question

5B

5 MINUTES
Aidan writes the counting numbers in order. In
Row 1, he writes the first number. In Row 2 he
writes the next two numbers, and so on as shown.
What is the thirteenth number in Row 16?
Row l: 1
Ron 2: 2 3
Row 3: 4 5 6
and so on...

Answer 1

133

Explanation:

There will be 16 numbers in row 16.

Now, first number of each row are
`1, 2, 4, 7, ..... , t_(16)`

So, the difference between the numbers is in the Arithmetic sequence.

Let, S₁₆ = 1 + 2 + 4 + 7 + ............ + t₁₆

And S₁₆ = 1 + 2 + 4 + 7 + .......+ t₁₅ + t₁₆

(-) --------------------------------------------------------------

0 = 1 + ( 1 + 2 + 3 + 4 + ...... up to 15 terms) - t₁₆ {Subtracting the equations}

⇒ t₁₆ = 1 + 0.5 (15)(15 + 1) = 121

Therefore, the first term of the 16th row is 121.

So, the 13th number of the 16th row will be = 121 + 12 = 133 (Answer)