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user100 [1]
2 years ago
11

Write down the first five terms of the geometric progression with

Mathematics
1 answer:
Vilka [71]2 years ago
7 0

Step-by-step explanation:

s1 = 3

s2 = 3×2 = 6

s3 = 6×2 = 12

s4 = 12×2 = 24

s5 = 24×2 = 48

sn = sn-1 × 2 = s1 × 2^(n-1)

s17 = 3 × 2¹⁶ = 3 × 65,536 = 196,608

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Step-by-step explanation:

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\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_{n+1}}{a_n}

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a_n=a_1\cdot \:r^{n-1}

a_n=5\left(-5\right)^{n-1}

a_{12}=5\left(-5\right)^{12-1}

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\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a

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\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}

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