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The ancient Greeks were very interested in number patterns. Triangular numbers are number that can be represented by a triangular array of dots, with n dots on each side. The first three triangular numbers are 1, 3, and 6.

Write a formula for the nth term of this sequence.

T(n) = [n(n + 1)] ÷ 2

Step-by-step explanation:

Sequence = 1, 3, 6

First term = 1

Second term = first term + 2 = 3

Third term = second term + 3 = 6

From the sequence :

Each successive term is doubled together with an increment of '1', that is;

Term 'n' : n(n + 1)

Then, the total is divided by the term 'n'.

Therefore, the nth term is expressed as

T(n) = [n(n + 1)] ÷ 2

For instance,

n = 1

T(1) = [1(1 + 1)] ÷ 2

T(1) = 1

n = 3

T(3) = [3(3 + 1)] ÷ 2

T(3) = 12 ÷ 2 = 6

The formula for the nth term of this sequence is

2^(n-1) + (n-1)

Step-by-step explanation: please find the attached file for the solution

step-by-step explanation: