Problem

Find the indicated terms of the arithmetic sequence with the given description.
The 50 th term is 1044 , and the common difference is 7 . Find the first and second terms.
\[
a_{1}=
\]
\[
a_{2}=
\]

Answer

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Answer

Solving the equation, we find that the second term of the sequence is \(\boxed{708}\)

Steps

Step 1 :Given that the 50th term (\(a_{50}\)) is 1044 and the common difference (\(d\)) is 7, we can use the formula for the nth term of an arithmetic sequence to find the first term (\(a_1\)): \[a_1 = a_{50} - (50-1)d\]

Step 2 :Substituting the given values into the formula, we get: \[a_1 = 1044 - (50-1)*7\]

Step 3 :Solving the equation, we find that the first term of the sequence is \(\boxed{701}\)

Step 4 :We can find the second term (\(a_2\)) by adding the common difference to the first term: \[a_2 = a_1 + d\]

Step 5 :Substituting the values we have, we get: \[a_2 = 701 + 7\]

Step 6 :Solving the equation, we find that the second term of the sequence is \(\boxed{708}\)

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