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Serga [27]
3 years ago
9

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 be

low.
A.682

B.2044

C.2048

D.678
Mathematics
2 answers:
umka2103 [35]3 years ago
6 0

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.

kvasek [131]3 years ago
4 0
The answer is 4+8+16+32+64+128+256+512+1024: This is equivalent to 2044
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