Question

write the 15th term of the pattern 11x-5​

Answer 1

Step-by-step explanation:

The rule for the sequence is as follows:

T0 = 2

Tn = 2 + sigma[q=1,q=n]{3 x 2^(q - 1)} ; if n>0

Where 2 is the 0th term (or T0), 5 is the 1st term (T1), 11 is the 2nd term (T2) and 23 is the 3rd term (T3).

In this case we are looking for the 4th/fourth term (T4) so here goes:

n = 4

and we plug n = 4 into our above equation/rule

T4 = 2 + sigma[q=1,q=4]{3 x 2^(q - 1)}

T4 = 2 + 3 x 2^3 + 3 x 2^2 + 3 x 2 + 3

T4 = 2 + 24 + 12 + 6 + 3

T4 = 47

But laugh out loud, after typing that all out on my phone i realised that there is a far simpler solution. You can write a relative rule for a sequence, it’s an equation so you can figure out the next term in a sequence as long as you ready have the previous term:

Tn = 2 x T(n-1) + 1

So each term is equal to double the previous term plus 1

So T4 = T3 x 2 + 1

T4 = 23 × 2 + 1

T4 = 47