Question

Find the seventh term of the geometric sequence 1, 2, 4, ... and the sum of the first seven terms. t7= S7=

Answer 1

Answer:

Seventh term is 64

Sum of the first seven terms is 127

Step-by-step explanation:

The common ratio is 2

$a_{n} = a_{1} r^{n - 1}$    

n = 7 and the first term is 1.  So,

$a_{7} = 1(2^{7 - 1} ) = 2^{6} = 64$

Seventh term is 64

$S_{n} = \frac{a_{1} (r^{n} -1)}{r - 1}$

$S_{7} = \frac{1(2^{7} -1)}{2 - 1}$

    $= \frac{128 - 1}{1} = 127$

Sum of the first seven terms is 127