# For a geometric sequence, t_7=5x+2 and t_10=x - 23. If the common ratio is 2, how do you find the value of t10?

Nov 24, 2015

If $r = 2$, then ${t}_{10} / {t}_{7} = {2}^{10 - 7} = {2}^{3} = 8$

#### Explanation:

If ${t}_{10} / {t}_{7} = 8$, then ...

$8 = \frac{x - 23}{5 x + 2}$

Now, solving for x ...

$x = - 1$

Finally we can find ${t}_{10} = x - 23 = - 1 - 23 = - 24$

hope that helped