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kykrilka [37]
2 years ago
11

Consider the arithmetic sequence log x + log √2, 2 log x + log 2, 3 log x + log 2√2......

Mathematics
1 answer:
likoan [24]2 years ago
8 0

Answer:

  • See below

Step-by-step explanation:

<u>Given sequence:</u>

  • log x + log√2, 2logx + log 2, 3logx + log2√2, ...

a)

<u>The terms can be rewritten as:</u>

  • T(1) = log x + log√2 = log x√2
  • T(2) = 2logx + log 2 = 2logx + 2 log√2 = 2log x√2
  • T(3) = 3logx + log2√2 = 3logx + 3log√2 = 3log x√2
  • ...
  • T(n) = n log x√2  (option A)

b)

<u>Sum of the first n terms:</u>

  • log x√2 + 2log x√2 + ... + nlog x√2 =
  • log x√2(1 + 2 + ... + n) =
  • log x√2 (1 + n)*n/2 =
  • 1/2n(n + 1)log x√2

<u>Sum of the first 40 terms:</u>

  • 1/2*40(40 + 1)log x√2 =
  • 820log x√2
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