Question

3. The first four terms of a sequence are:

T2 = 12+ 22
T3 = 12 + 22 + 32
T4 = 12 + 22 + 32 +42
T1 = 12
The n" term is given by Tn=n(n + 1)(2n + 1).
Work out the value of T23.

Answer 1

The 23rd term is 2806.

Explanation:

The other answerer has used the formula but i'm answering from the assumption that T1 to T4 are correct.

Each term is the sum of n terms of an arithmetic series with first term a1 = 12 and common difference d = 10.

Sum of n terms = (n/2)[2a1 + d(n - 1)]

So the sum of 23 terms =

= 23/2 (2*12 + 10 * 22)

= 11.5 * 244

= 2806.

Answer 2

Explanation:

tn=n(n+1)(2n+1)

t23=23(23+1)(2*23+1)

t23=36754