The triangular numbers are the following: T1 = 1, T2 = 3, T3 = 6, T4 = 10, ... They are called triangular numbers because you can think of the number as a series of dots which can be arranged into a triangle as shown below:
T1 =1
T2 = 3
T3=6
T4=10

The formula for the nth triangular number is Tn = n(n+1)/2. For example, the fourth triangular number is 10, so T4 = 10.

1953 is a triangular number. Which one is it?

For example, if 1953 happened to be the 4th triangular number (which of course it's not), your answer would be 4.

T62

Step-by-step explanation:

Tn = n(n + 1)/2

1953 = n(n + 1)/2

n(n + 1) = 3906

n^2 + n - 3906 = 0

(n + 63)(n - 62) = 0

n = -63 or n = 62

T62

step-by-step explanation:

here's what happens:

1) the graph of f   = x^2 is shifted 2 units to the right.

2) the resulting graph is reflected in the x-axis, so that the parabola now opens down.

3) this final result is transformed up by 5 units.

the terms of a geometric sequence can be found by beginning with the first term and multiplying by the common ratio repeatedly. a recursive formula for a geometric sequence with common ratio r is given by an=ran−1 a n = r a n − 1 for n≥2 n ≥ 2 .

step-by-step explanation: