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Find an explicit formula for the arithmetic sequence −2ext,−14ext,−26ext,−38-2 ext{,} -14 ext{,} -26 ext{,} -38 . Note: the first term should be d(1)d(1) .

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Q. Find an explicit formula for the arithmetic sequence −2ext,−14ext,−26ext,−38-2 ext{,} -14 ext{,} -26 ext{,} -38 . Note: the first term should be d(1)d(1) .
  1. Identify Terms: Identify the first term and common difference of the sequence.\newlineThe first term d(1)d(1) is −2-2.\newlineTo find the common difference, subtract the first term from the second term: −14−(−2)=−12-14 - (-2) = -12.
  2. Arithmetic Sequence Formula: Write the formula for the nnth term of an arithmetic sequence.\newlineThe formula is d(n)=d(1)+(n−1)⋅dd(n) = d(1) + (n - 1) \cdot d, where dd is the common difference.
  3. Substitute Values: Substitute the values of d(1)d(1) and dd into the formula.\newlined(n)=−2+(n−1)×(−12)d(n) = -2 + (n - 1) \times (-12).\newlineSimplify the formula: d(n)=−2−12n+12d(n) = -2 - 12n + 12.\newlineFurther simplification gives: d(n)=−12n+10d(n) = -12n + 10.

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