The 4th term of a geometric sequence is 192.if the first term is 3 then find the common ratio and the number of terms that will give a sum of 255

3r^3 = 192

so r = 4
So now find n such that
3(4^n - 1)/(4-1) = 255

Did you know?

Did you know that in a geometric sequence, each term is found by multiplying the previous term by a constant factor called the common ratio? In the case where the 4th term is 192 and the first term is 3, we can find the common ratio by dividing the 4th term by the first term. This gives us a common ratio of 192/3 = 64. Now, suppose we want to find the number of terms that will give a sum of 255. To find this, we can use the formula for the sum of a geometric series. Rearranging the formula, we have the number of terms is equal to the logarithm of (sum/first term) divided by the logarithm of the common ratio. Plugging in the values, the number of terms will be equal to log(255/3) / log(64). By evaluating this expression, we can determine how many terms will give a sum of 255.