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Find the 76 th term of the arithmetic sequence -26,-41,-56,dots Answer:

Find the 7676 th term of the arithmetic sequence −26,−41,−56,… -26,-41,-56, \ldots \newlineAnswer:

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Full solution

Q. Find the 7676 th term of the arithmetic sequence −26,−41,−56,… -26,-41,-56, \ldots \newlineAnswer:
  1. Identify common difference: Identify the common difference in the arithmetic sequence.\newlineThe common difference dd is the difference between any two consecutive terms.\newlineFor the given sequence: −41−(−26)=−41+26=−15-41 - (-26) = -41 + 26 = -15
  2. Use formula for nth term: Use the formula for the nth term of an arithmetic sequence.\newlineThe nth term ana_n of an arithmetic sequence can be found using the formula:\newlinean=a1+(n−1)da_n = a_1 + (n - 1)d\newlinewhere a1a_1 is the first term and dd is the common difference.
  3. Calculate 7676th term: Calculate the 7676th term using the formula.\newlinea76=a1+(76−1)(−15)a_{76} = a_1 + (76 - 1)(-15)\newlinea76=−26+75(−15)a_{76} = -26 + 75(-15)
  4. Perform multiplication and addition: Perform the multiplication and addition to find the 76th76^{\text{th}} term.a76=−26+(75×−15)a_{76} = -26 + (75 \times -15)a76=−26−1125a_{76} = -26 - 1125a76=−1151a_{76} = -1151

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