answer:Rene's sister has 50 + 2 = 52 dolls. Rene has 3 * 52 = 156 dolls. Altogether, they have 50 + 52 + 156 = 258 dolls. 258 The answer is: 258

answer:To prompt the user to enter both the cell location and the value they want to add to the cell, we can modify the Swift code as follows: ```swift // import necessary libraries import Foundation import GoogleSignIn // create GIDSignIn object let signIn = GIDSignIn.sharedInstance() // define scopes for authorization let scopes = [https://www.googleapis.com/auth/spreadsheets] // prompt user to enter cell location print(Enter cell location (e.g. A1):) let cellLocation = readLine() ?? // prompt user to enter value print(Enter value to add:) let userValue = readLine() ?? // authenticate user signIn?.scopes = scopes signIn?.signIn() // create query to read specified cell let query = GTLRSheetsQuery_SpreadsheetsValuesGet.query(withSpreadsheetId: your_spreadsheet_id, range: Sheet1!(cellLocation)) // execute query to get cell value service.executeQuery(query) { (ticket, response, error) in guard error == nil else { print(Error: (error?.localizedDescription ?? )) return } guard let valueRange = response as? GTLRSheets_ValueRange else { print(Error: No value range found.) return } guard let cellValue = valueRange.values?.first?.first as? String else { print(Error: No cell value found.) return } // add user value to cell value let newValue = Int(cellValue)! + Int(userValue)! // create update query let updateQuery = GTLRSheetsQuery_SpreadsheetsValuesUpdate.query(withObject: GTLRSheets_ValueRange.init(values: [[newValue]]), spreadsheetId: your_spreadsheet_id, range: Sheet1!(cellLocation)) // execute update query to update cell with new value service.executeQuery(updateQuery) { (ticket, response, error) in guard error == nil else { print(Error: (error?.localizedDescription ?? )) return } print(Cell updated successfully.) } } ``` The code now prompts the user to enter the cell location and value to add using the `readLine()` function. These values are then used to create the query to read the specified cell and update it with the new value.

answer:To find the general formula for the nth term of the sequence, let's first express the sequence in terms of the differences between consecutive terms. We notice that the sequence of differences between consecutive terms is simply the sequence of natural numbers, i.e., 1, 2, 3, 4, 5, and so on. With this insight, we can express the nth term of the sequence as a sum. The nth term is the result of adding the first (n-1) natural numbers to the initial term, which is 1. The sum of the first k natural numbers can be expressed as k(k+1)/2. Now, the nth term can be written as 1 + (sum of first (n-1) natural numbers). This simplifies to 1 + (n-1)(n)/2. Further simplification gives us the formula for the nth term: n(n-1)/2 + 1, or equivalently, (n^2 - n + 2)/2. However, to ensure this formula is indeed correct, let's also consider an alternative derivation. We can express the sequence using a recurrence relation. By expressing a few terms explicitly and using mathematical induction, we can confirm that the general formula we derived above is indeed the correct one. Both approaches converge on the same formula: the nth term of the sequence is given by (n^2 - n + 2)/2. This demonstrates the power of mathematical thinking in tackling sequence problems, often allowing for multiple paths to the solution.

answer:Let's reconsider the sequence and look for an even more elegant approach. Notice that the sequence can be rewritten by focusing on the relationship between the terms and the triangular numbers. The sequence is essentially formed by adding consecutive natural numbers to the initial term, 1. Now, think about constructing this sequence term by term. At each step, the increment added to the previous term increases by 1. This hints at a relationship with triangular numbers, which are sums of consecutive integers. Specifically, the nth triangular number is given by the formula T(n) = n(n+1)/2. Now, observe that our sequence essentially consists of terms that are each 1 more than the corresponding triangular number, but shifted by one position. Using this insight, we can elegantly express the nth term of the sequence as T(n-1) + 1 = (n-1)n/2 + 1 = (n^2 - n + 2)/2. This approach bypasses the need for explicit summation or recursive formulation, providing an even more streamlined path to the general formula for the sequence.