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* r^8=1024\\\\\Rightarrow r^8=(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\\\\\\=(a(r^9-1))/(r-1)\\\\\\=(4*(2^9-1))/(2-1)\\\\\\=(4*(512-1))/(1)\\\\=4*511\\\\=2044.`

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

Option (B) is CORRECT.