Question

what is the 11th term of the sequence 1,2,4,8,16

answer choices
32
192
1024
2048

Answer 1

Begin by adding each number by the same number. The sum is then added by its number. Continue to do this method until you reach the eleventh term. Remember to include the first term. 

1 + 1 = 2 - first term
2 + 2 = 4 - second term
4 + 4 = 8 - third term
8 + 8 = 16 - fourth term...
16 + 16 = 32
32 + 32 = 64
64 + 64 = 128
128 + 128 = 256
256 + 256 = 512
512 + 512 = 1024
1024 + 1024 = 2048 - eleventh term

Answer 2

The 11th term of the given geometric sequence is equal to 2048.

Given the following data:

• First (1st) term = 1

• Second term = 2

To calculate the 11th term of the given geometric sequence:

Mathematically, the nth term of an geometric sequence is given by the formula:

$a_n = ar^{n-1}$  ...equation 1.

Where:

• r is the common ratio.

• a is the first term of an geometric sequence.

First of all, we would determine the common ratio as follows:

$r=\frac{T_n}{T_{n-1}}\\\\r=\frac{2}{1}$

r = 2

Substituting the values into eqn. 1, we have:

$a_{11} = 1 \times 2^{11-1}\\\\a_{11} = 2^{10}\\\\a_{11} =2048$

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