Question

find the next two terms in the sequence 11,7,3,-1

Answer 1

-5 and -9
The pattern is subtracting 4 from the previous number

11 -4 = 7
7 - 4 = 3
3 - 4 = -1
-1 - 4 = -5
-5 - 4 = -9

Answer 2

When a sequence has a common difference, then the sequence is arithmetic

The next two terms are -5 and -9

The sequence is given as: 11, 7, 3, -1

The above sequence have a common difference.

This is calculated by subtracting a term from the next term.

i.e.

$\mathbf{d = T_2 - T_1 = T_3 - T_2 = T_{n+1} - T_n}$

So, we have:

$\mathbf{d = 7 - 11}$

$\mathbf{d = -4}$

The nth term of an arithmetic sequence is:

$\mathbf{T_n = T_1 + (n - 1)d}$

So, we have:

$\mathbf{T_n = 11 + (n - 1)(-4)}$

$\mathbf{T_n = 11 -4n +4}$

Evaluate like terms

$\mathbf{T_n = 15 -4n }$

The next two terms are the 5th and the 6th terms.

So, we have:

$\mathbf{T_5 = 15 -4 \times 5 = -5}$

$\mathbf{T_6 = 15 -4 \times 6 = -9}$

Hence, the next two terms are -5 and -9

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