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Google Classroom Microsoft Teams You might need: 囲 Calculator Find an explicit formula for the arithmetic sequence -2,-14,-26,-38,dots.. Note: the first term should be d(1). d(n)= ◻ Show Calculator

Google Classroom\newlineMicrosoft Teams\newlineYou might need: 囲 Calculator\newlineFind an explicit formula for the arithmetic sequence −2,−14,−26,−38,… -2,-14,-26,-38, \ldots ..\newlineNote: the first term should be d(1) d(1) .\newlined(n)= d(n)= \newline□ \square \newlineShow Calculator

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Q. Google Classroom\newlineMicrosoft Teams\newlineYou might need: 囲 Calculator\newlineFind an explicit formula for the arithmetic sequence −2,−14,−26,−38,… -2,-14,-26,-38, \ldots ..\newlineNote: the first term should be d(1) d(1) .\newlined(n)= d(n)= \newline□ \square \newlineShow Calculator
  1. Identify sequence type: Identify the type of sequence.\newlineThe sequence given is −2-2, −14-14, −26-26, −38-38, ...\newlineTo determine if it's arithmetic, check the difference between consecutive terms.\newlineDifference = −14−(−2)=−12-14 - (-2) = -12\newlineDifference = −26−(−14)=−12-26 - (-14) = -12\newlineSince the difference is constant, the sequence is arithmetic.
  2. Find first term and difference: Find the first term and common difference.\newlineThe first term (d1d_1) is −2-2.\newlineThe common difference (dd) is −12-12, as calculated previously.
  3. Write nth term formula: Write the formula for the nth term of an arithmetic sequence.\newlineThe formula for the nth term (dnd_n) of an arithmetic sequence is:\newlinedn=d1+(n−1)⋅dd_n = d_1 + (n - 1) \cdot d\newlineSubstitute d1=−2d_1 = -2 and d=−12d = -12 into the formula:\newlinedn=−2+(n−1)⋅(−12)d_n = -2 + (n - 1) \cdot (-12)
  4. Simplify the formula: Simplify the formula.\newlinedn=−2−12×(n−1)d_n = -2 - 12 \times (n - 1)\newlinedn=−2−12n+12d_n = -2 - 12n + 12\newlinedn=10−12nd_n = 10 - 12n

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