For each of the following sequences,

• list the first 6 terms of the sequence.
• provide an explicit formula describing the n-th term of the sequence.
• describe the sequence using a recurrence relation.

Assume that cach sequence starts at index 0 and that they are defined for all neN.

1(a) {ax} is a geometric sequence with the initial term 8 and the common ratio 2.
1(b) {bk} is an arithmetic sequence with the initial term 0 and the common difference 2.
1(e) {cx} is a sequence where the k-th term is the k-th power of 3 and the initial term is 1.
1(d) {dx} is a sequence where the k-th term is the sum of the first k + 1 positive odd numbers and the initial term is 1.

Problem 2. Prove that {ck} (from 1(c)) is an increasing sequence.

Which of the following is not a potential problem with beta and its estimation? sometimes, during a period when the company is undergoing a change such as toward more leverage or riskier assets, the calculated beta will be drastically different than the "true" or "expected future" beta. the beta of "the market," can change over time, sometimes drastically.

You have just been hired as a financial analyst for barrington industries. unfortunately, company headquarters (where all of the firm's records are kept) has been destroyed by fire. so, your first job will be to recreate the firm's cash flow statement for the year just ended. the firm had $100,000 in the bank at the end of the prior year, and its working capital accounts except cash remained constant during the year. it earned $5 million in net income during the year but paid $800,000 in dividends to common shareholders. throughout the year, the firm purchased $5.5 million of machinery that was needed for a new project. you have just spoken to the firm's accountants and learned that annual depreciation expense for the year is $450,000; however, the purchase price for the machinery represents additions to property, plant, and equipment before depreciation. finally, you have determined that the only financing done by the firm was to issue long-term debt of $1 million at a 6% interest rate. what was the firm's end- of-year cash balance? recreate the firm's cash flow statement to arrive at your answer

Computing equivalent units is especially important for: (a) goods that take a relatively short time to produce, such as plastic bottles. (b) goods with sustainability implications in their production processes. (c) goods that are started and completed during the same period. (d) goods that take a long time to produce, such as airplanes.