Question

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

Answer 1

Answer:

• See below

Step-by-step explanation:

Given sequence:

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

a)

The terms can be rewritten as:

• 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)

Sum of the first n terms:

• 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

Sum of the first 40 terms:

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