Question

Find the sum of a 9-term geometric sequence when the first term is 4 and the last term is 1,024 and select the correct answer below.


A.682

B.2044

C.2048

D.678

Answer 1

The answer is 4+8+16+32+64+128+256+512+1024: This is equivalent to 2044

Answer 2

Answer:  The correct option is (B) 2044.

Step-by-step explanation:  We are given to find the sum of a 9-term geometric sequence when the first term is 4 and the last term is 1,024.

We know that

the n-th term of a geometric sequence with first term a and common ratio r is given by

$a_n=ar^{n-1}.$

According to the given information, we have

$a=4$

and

$ar^{9-1}=1024\\\\\Rightarrow 4\times r^8=1024\\\\\Rightarrow r^8=\dfrac{1024}{4}\\\\\Rightarrow r^8=256\\\\\Rightarrow r^8=2^8\\\\\Rightarrow r=2.$

Therefore, the sum of the 9-term geometric sequence is given by

$S_9\\\\\\=\dfrac{a(r^9-1)}{r-1}\\\\\\=\dfrac{4\times(2^9-1)}{2-1}\\\\\\=\dfrac{4\times(512-1)}{1}\\\\=4\times511\\\\=2044.$

Thus, the required sum of the 9-term sequence is 2044.

Option (B) is CORRECT.