Find the next number in the sequence: 1, 5, 11, 19, 28, __

Here are the solutions to the questions: 7. Find the next number in the sequence below. 1, 5, 11, 19, 28, __ Step 1: Find the differences between consecutive terms. 5 - 1 = 4 11 - 5 = 6 19 - 11 = 8 28 - 19 = 9 The sequence of first differences is 4, 6, 8, 9. Step 2: Find the differences between these first differences (second differences). 6 - 4 = 2 8 - 6 = 2 9 - 8 = 1 The sequence of second differences is 2, 2, 1. Step 3: Identify the pattern in the second differences. The increment is decreasing by 1 each time (from +2 to +1). Assuming this pattern continues, the next second difference would be 1 - 1 = 0. Step 4: Use the next second difference to find the next first difference. The last first difference was 9. Adding the next second difference (0) gives 9 + 0 = 9. So, the next first difference is 9. Step 5: Add the next first difference to the last term in the sequence to find the next number. The last term was 28. Adding the next first difference (9) gives 28 + 9 = 37. The next number in the sequence is 37. 8. Express 7800 in scientific notation. Step 1: Move the decimal point to the left until there is only one non-zero digit to its left. For 7800, the decimal point is after the last zero. Move it 3 places to the left to get 7.8. Step 2: Count the number of places the decimal point was moved. This number will be the exponent of 10. Since it was moved 3 places to the left, the exponent is 3. 7800 = 7.8 × 10^3 In scientific notation, 7800 is 7.8 × 10^3. 9. Expand 9658 using exponents. Step 1: Break down the number into its place values. 9658 consists of 9 thousands, 6 hundreds, 5 tens, and 8 ones. Step 2: Express each place value using powers of 10. 9658 = (9 × 1000) + (6 × 100) + (5 × 10) + (8 × 1) 9658 = (9 × 10^3) + (6 × 10^2) + (5 × 10^1) + (8 × 10^0) The expanded form using exponents is $