Question

Find the 7th term in the sequence with the following definition: a1 = 64 | 0

Answer 1

Given:

The first term of the sequence is $a_1=64$

The nth term of the sequence is $a_n=\frac{a_{n-1}}{2}$

We need to determine the 7th term of the sequence.

Second term:

Substituting n = 2 in the nth term of the sequence, we get;

$a_2=\frac{a_{2-1}}{2}$

$a_2=\frac{a_{1}}{2}$

$a_2=\frac{64}{2}$

$a_2=32$

Thus, the second term of the sequence is 32.

Third term:

Substituting n = 3 in the nth term of the sequence, we get;

$a_3=\frac{a_{3-1}}{2}$

$a_3=\frac{32}{2}$

$a_3=16$

Thus, the third term of the sequence is 16.

Fourth term:

Substituting n = 4 in the nth term of the sequence, we get;

$a_4=\frac{a_{4-1}}{2}$

$a_4=\frac{16}{2}$

$a_4=8$

Thus, the fourth term of the sequence is 8.

Fifth term:

Substituting n = 5 in the nth term of the sequence, we get;

$a_5=\frac{a_{5-1}}{2}$

$a_5=\frac{8}{2}$

$a_5=4$

Thus, the fifth term of the sequence is 4.

Sixth term:

Substituting n = 6 in the nth term of the sequence, we get;

$a_6=\frac{a_{6-1}}{2}$

$a_6=\frac{4}{2}$

$a_6=2$

Thus, the sixth term of the sequence is 2.

Seventh term:

Substituting n = 7 in the nth term of the sequence, we get;

$a_7=\frac{a_{7-1}}{2}$

$a_7=\frac{2}{2}$

$a_7=1$

Thus, the seventh term of the sequence is 1.