Find the 9th Term 10 , 20 , 40 , 80 , 160 , 320 , 640 , 1280

$10$ , $20$ , $40$ , $80$ , $160$ , $320$ , $640$ , $1280$

Step 1

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by $2$ gives the next term. In other words, $a_{n} = a_{1} r^{n - 1}$ .

Geometric Sequence: $r = 2$

Step 2

This is the form of a geometric sequence.

$a_{n} = a_{1} r^{n - 1}$

Step 3

Substitute in the values of $a_{1} = 10$ and $r = 2$ .

$a_{n} = 10 \cdot 2^{n - 1}$

Step 4

Substitute in the value of $n$ to find the $n$ th term.

$a_{9} = 10 \cdot 2^{(9) - 1}$

Step 5

Subtract $1$ from $9$ .

$a_{9} = 10 \cdot 2^{8}$

Step 6

Raise $2$ to the power of $8$ .

$a_{9} = 10 \cdot 256$

Step 7

Multiply $10$ by $256$ .

$a_{9} = 2560$

Find the 9th Term 10 , 20 , 40 , 80 , 160 , 320 , 640 , 1280

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