Crank out the common ratio, first term, and last term of the sequence. *r *= 2
*a*_{1} = 1
*a*_{n} = 131,072
Use the information you've gathered and the general rule of a geometric
sequence to create an equation with one variable,* n*. That's our total number of terms. *a*_{n} = *a*_{1}(*r*)^{n –}^{ 1}
131,072 = 1(2)^{n }^{– 1} Solve the equation you've created for *n*. 131,072 = (2)^{n }^{– 1} Rewrite the equation as a logarithm with a base of 2 to solve for *n* using a calculator. log_{2}(131,072) = *n* – 1 17 = *n* – 1
*n *= 18 Guess and check works as well if you're not into the whole logarithm scene. 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
Either way, it turns out we've got 18 terms in the sequence. |