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Find the 72 nd term of the arithmetic sequence -23,-39,-55,dots Answer:

Find the 72nd 72 n d term of the arithmetic sequence −23,−39,−55,… -23,-39,-55, \ldots \newlineAnswer:

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Full solution

Q. Find the 72nd 72 n d term of the arithmetic sequence −23,−39,−55,… -23,-39,-55, \ldots \newlineAnswer:
  1. Arithmetic Sequence Formula: To find the 72nd72^{nd} term of an arithmetic sequence, we need to use the formula for the nthn^{th} term of an arithmetic sequence, which is:\newlinean=a1+(n−1)da_n = a_1 + (n - 1)d\newlinewhere ana_n is the nthn^{th} term, a1a_1 is the first term, nn is the term number, and dd is the common difference between the terms.
  2. Identify First Term: First, we identify the first term a1a_1 of the sequence, which is given as −23-23.
  3. Find Common Difference: Next, we need to find the common difference dd. We can do this by subtracting the first term from the second term:\newlined=−39−(−23)=−39+23=−16d = -39 - (-23) = -39 + 23 = -16
  4. Calculate 7272nd Term: Now that we have the first term and the common difference, we can find the 7272nd term a72a_{72} using the formula:\newlinea72=a1+(72−1)da_{72} = a_1 + (72 - 1)d
  5. Substitute Values: Substitute the known values into the formula:\newlinea72=−23+(72−1)(−16)a_{72} = -23 + (72 - 1)(-16)\newlinea72=−23+(71)(−16)a_{72} = -23 + (71)(-16)
  6. Perform Calculation: Now, perform the multiplication and addition to find a72a_{72}:\newlinea72=−23+(−1136)a_{72} = -23 + (-1136)\newlinea72=−1159a_{72} = -1159

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