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Find the 6 th term of the arithmetic sequence x+5,4x+7,7x+9,dots Answer:

Find the 66 th term of the arithmetic sequence x+5,4x+7,7x+9,… x+5,4 x+7,7 x+9, \ldots \newlineAnswer:

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Q. Find the 66 th term of the arithmetic sequence x+5,4x+7,7x+9,… x+5,4 x+7,7 x+9, \ldots \newlineAnswer:
  1. Identify common difference: Identify the common difference of the arithmetic sequence.\newlineTo find the common difference, we subtract the first term from the second term.\newlineCommon difference dd = (4x+7)−(x+5)(4x + 7) - (x + 5)\newlined=4x+7−x−5d = 4x + 7 - x - 5\newlined=3x+2d = 3x + 2
  2. Find nth term formula: Use the common difference to find the nth term formula.\newlineThe nth term of an arithmetic sequence can be found using the formula:\newlinenth term = first term + (n−1)×common difference(n - 1) \times \text{common difference}\newlineWe already have the first term (x+5)(x + 5) and the common difference (3x+2)(3x + 2).
  3. Calculate 66th term: Calculate the 66th term using the nth term formula.\newline66th term =(x+5)+(6−1)×(3x+2)= (x + 5) + (6 - 1) \times (3x + 2)\newline66th term =(x+5)+5×(3x+2)= (x + 5) + 5 \times (3x + 2)\newline66th term =(x+5)+(15x+10)= (x + 5) + (15x + 10)\newline66th term =x+5+15x+10= x + 5 + 15x + 10\newline66th term =16x+15= 16x + 15

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