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QuestionFind the 70th term of the sequence 29,17,5,…29, 17, 5, \ldots

Studdy Solution

STEP 1

Assumptions1. The given sequence is an arithmetic sequence. . The first term (a) of the sequence is29.
3. The common difference (d) of the sequence can be found by subtracting the first term from the second term.
4. The70th term (70) can be found using the formula for the nth term of an arithmetic sequencen = a + (n-1)d

STEP 2

First, we need to find the common difference of the arithmetic sequence. We can do this by subtracting the first term from the second term.
d=Term2−Term1d = Term2 - Term1

STEP 3

Now, plug in the given values for the first and second terms to calculate the common difference.
d=17−29d =17 -29

STEP 4

Calculate the common difference.
d=17−29=−12d =17 -29 = -12

STEP 5

Now that we have the common difference, we can find the70th term of the sequence using the formula for the nth term of an arithmetic sequence.
n=a+(n−1)dn = a + (n-1)d

STEP 6

Plug in the values for the first term, the common difference, and n=70 to calculate the70th term.
70=29+(70−1)(−12)70 =29 + (70-1)(-12)

STEP 7

implify the expression inside the parentheses.
70=29+69(−12)70 =29 +69(-12)

STEP 8

Perform the multiplication.
70=29−82870 =29 -828

STEP 9

Calculate the70th term.
70=29−828=−79970 =29 -828 = -799The70th term of the arithmetic sequence is -799.

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