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Find the sum of the first 7 terms of the following series, to the nearest integer. 8,6,(9)/(2),dots Answer:

Find the sum of the first 77 terms of the following series, to the nearest integer.\newline8,6,92,… 8,6, \frac{9}{2}, \ldots \newlineAnswer:

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Q. Find the sum of the first 77 terms of the following series, to the nearest integer.\newline8,6,92,… 8,6, \frac{9}{2}, \ldots \newlineAnswer:
  1. Identify pattern: Identify the pattern in the series.\newlineThe series starts with 88, then 66, then 92\frac{9}{2}. To find the pattern, we need to determine how each term is related to the previous one.\newline88 to 66 is a decrease of 22.\newline66 to 92\frac{9}{2} (which is 4.54.5) is a decrease of 1.51.5.\newlineIt seems that the series is decreasing by a constant difference of 6600 each time.
  2. Calculate difference: Calculate the common difference.\newlineThe common difference is the amount subtracted from each term to get the next term. From the pattern identified in Step 11, the common difference is −0.5-0.5.
  3. Write first 77 terms: Write down the first 77 terms using the common difference.\newline11st term: 88\newline22nd term: 8−0.5=7.58 - 0.5 = 7.5\newline33rd term: 7.5−0.5=77.5 - 0.5 = 7\newline44th term: 7−0.5=6.57 - 0.5 = 6.5\newline55th term: 6.5−0.5=66.5 - 0.5 = 6\newline66th term: 6−0.5=5.56 - 0.5 = 5.5\newline77th term: 5.5−0.5=55.5 - 0.5 = 5
  4. Sum first 77 terms: Sum the first 77 terms.\newlineSum = 8+7.5+7+6.5+6+5.5+58 + 7.5 + 7 + 6.5 + 6 + 5.5 + 5\newlineSum = 45.545.5
  5. Round sum: Round the sum to the nearest integer.\newlineThe sum of the first 77 terms is 45.545.5, which rounds to 4646 when rounded to the nearest integer.

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