Find the n th partial sum of the geometric sequence. 1 , − 4 , 16 , − 64 , 256 , … , n = 7 1,-4,16,-64,256, \ldots, \quad n=7 1 , − 4 , 16 , − 64 , 256 , … , n = 7 A) 3326B) 3277C) -819D) 3620E) -51

Question

Find the n th partial sum of the geometric sequence.   1 , − 4 , 16 , − 64 , 256 , … , n = 7 1,-4,16,-64,256, \ldots, \quad n=7 1 , − 4 , 16 , − 64 , 256 , … , n = 7 A) 3326B) 3277C) -819D) 3620E) -51

Brooklyn Fields · Accepted Answer

Final Answer : B, Explanation :   The given sequence is a geometric sequence with the first term   a = 1 a = 1 a = 1   and common ratio   r = − 4 r = -4 r = − 4  . The nth partial sum of a geometric sequence is given by the formula   S n = a ( 1 − r n ) 1 − r S_n = \frac{a(1 - r^n)}{1 - r} S n ​ = 1 − r a ( 1 − r n ) ​   when   r ≠ 1 r 
eq 1 r  = 1  . Substituting   a = 1 a = 1 a = 1  ,   r = − 4 r = -4 r = − 4  , and   n = 7 n = 7 n = 7  , we get   S 7 = 1 ( 1 − ( − 4 ) 7 ) 1 − ( − 4 ) = 1 − ( − 16384 ) 5 = 16385 5 = 3277 S_7 = \frac{1(1 - (-4)^7)}{1 - (-4)} = \frac{1 - (-16384)}{5} = \frac{16385}{5} = 3277 S 7 ​ = 1 − ( − 4 ) 1 ( 1 − ( − 4 ) 7 ) ​ = 5 1 − ( − 16384 ) ​ = 5 16385 ​ = 3277  .

Find the n th partial sum of the geometric sequence. $\ldots, \quad n=7$

A) 3326
B) 3277
C) -819
D) 3620
E) -51

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Learning Objectives

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Find the n th partial sum of the geometric sequence. 1,−4,16,−64,256,…,n=71,-4,16,-64,256, \ldots, \quad n=71,−4,16,−64,256,…,n=7 A) 3326B) 3277C) -819D) 3620E) -51

Definitions

Learning Objectives

Learning Objectives

Related questions

Find the n th partial sum of the geometric sequence. $\ldots, \quad n=7$

A) 3326
B) 3277
C) -819
D) 3620
E) -51