*r *= 2
*a*_{1} = 1
*a*_{n} = 131,072
Locate the common ratio, first term, and last term of the sequence. *a*_{n} = *a*_{1}( *r* )^{n¬-1} 131,072 = 1(2)^{n¬-1}
Use the information you've gathered and the general rule of a geometric sequence to create an equation with one variable, the number of terms*, n*. 131,072 = 1(2)^{n-1} 131,072 = (2)^{n-1} Solve the equation you've created for the number of terms in the sequence, *n*. log_{2}(131,072) = *n* – 1 17 = *n* – 1
*n *= 18 Rewrite the equation as a logarithm with a base of 2 to solve for *n* using a calculator. 2^{n-1} = ? 2^{16-1} = 2^{15} = 32,768 2^{17-1} = 2^{16} = 65,536 2^{18-1} = 2^{17 }= 131, 072 *n *= 18
Guess and check works as well if you're not into the whole logarithm scene. |