Find the 8th Term 2 , 10 , 50 , 250 , 1250 , 6250

$2$ , $10$ , $50$ , $250$ , $1250$ , $6250$

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 $5$ gives the next term. In other words, $a_{n} = a_{1} r^{n - 1}$ .

Geometric Sequence: $r = 5$

Step 2

This is the form of a geometric sequence.

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

Step 3

Substitute in the values of $a_{1} = 2$ and $r = 5$ .

$a_{n} = 2 \cdot 5^{n - 1}$

Step 4

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

$a_{8} = 2 \cdot 5^{(8) - 1}$

Step 5

Subtract $1$ from $8$ .

$a_{8} = 2 \cdot 5^{7}$

Step 6

Raise $5$ to the power of $7$ .

$a_{8} = 2 \cdot 78125$

Step 7

Multiply $2$ by $78125$ .

$a_{8} = 156250$

Find the 8th Term 2 , 10 , 50 , 250 , 1250 , 6250

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