The geometric mean of the numbers 2, 8, 16, 128, 512 is

Question

The geometric mean of the numbers 2, 8, 16, 128, 512 is (A) 133.2 (B) (5/(1)2+(1)8+(1/16)+(1/128)+(1/512) (C) 224/5 (D) none of these

Tardigrade Admin · Accepted Answer

Required geometric mean = (2×8× 16× 128× 512)1/5 (note that there are 5 items and each item is a power of 2) = (21 × 23× 24× 27× 29)1/5 = (21+3+4+7+9)1/5 =224/5

Q. The geometric mean of the numbers 2, 8, 16, 128, 512 is

133.2

$\frac{5}{\frac{1}{2} + \frac{1}{8} + \frac{1}{16} + \frac{1}{128} + \frac{1}{512}}$

$2^{24/5}$

none of these

Required geometric mean
$= (2 \times 8 \times 16 \times 128 \times 512)^{1/5}$
(note that there are 5 items and each item is a power of 2) $= (2^{1} \times 2^{3} \times 2^{4} \times 2^{7} \times 2^{9})^{1/5} = (2^{1 + 3 + 4 + 7 + 9})^{1/5}$ $= 2^{24/5}$

Q. The geometric mean of the numbers 2, 8, 16, 128, 512 is

133.2

21​+81​+161​+1281​+5121​5​

224/5

none of these

Required geometric mean =(2×8×16×128×512)1/5 (note that there are 5 items and each item is a power of 2) =(21×23×24×27×29)1/5=(21+3+4+7+9)1/5=224/5

$\frac{5}{\frac{1}{2} + \frac{1}{8} + \frac{1}{16} + \frac{1}{128} + \frac{1}{512}}$

$2^{24/5}$

Required geometric mean
$= (2 \times 8 \times 16 \times 128 \times 512)^{1/5}$
(note that there are 5 items and each item is a power of 2) $= (2^{1} \times 2^{3} \times 2^{4} \times 2^{7} \times 2^{9})^{1/5} = (2^{1 + 3 + 4 + 7 + 9})^{1/5}$ $= 2^{24/5}$