eattern is $$ 5,10,20,40 \ldots $$. Find the 8 th term of the pattern

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UpStudy AI · Accepted Answer

The given pattern is $$ 5, 10, 20, 40, \ldots $$.

To identify the pattern, let's analyze the terms:

- The first term is $$ 5 $$.
- The second term is $$ 10 $$ which is $$ 5 \times 2 $$.
- The third term is $$ 20 $$ which is $$ 10 \times 2 $$.
- The fourth term is $$ 40 $$ which is $$ 20 \times 2 $$.

From this, we can see that each term is obtained by multiplying the previous term by $$ 2 $$.

Thus, the $$ n $$-th term can be expressed as:
$$
a_n = 5 \times 2^{(n-1)}
$$

Now, we need to find the 8th term, $$ a_8 $$:
$$
a_8 = 5 \times 2^{(8-1)} = 5 \times 2^7
$$

Now, let's calculate $$ 2^7 $$:
$$
2^7 = 128
$$

Now, substituting back:
$$
a_8 = 5 \times 128 = 640
$$

Therefore, the 8th term of the pattern is $$ 640 $$.
The 8th term of the pattern is 640.

eattern is \( 5,10,20,40 \ldots \). Find the 8 th term of the pattern

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