Given a_17=-82, d=-3a17=−82,d=−3, how do you find a_24a24?

1 Answer
marfre
Mar 2, 2017

a_24 = -93a24=−93

Explanation:

Find the first element of the sequence using the formula for arithmetic sequences: a_n = a_1 + (n-1)dan=a1+(n−1)d

a_17 = -82 = a_1 + (17-1)(-3)a17=−82=a1+(17−1)(−3)
-82 = a_1 + 16(-3)−82=a1+16(−3)
-82 = a_1 -48−82=a1−48
-82+48 = a_1 -48+48−82+48=a1−48+48
a_1 = -82 + 48a1=−82+48
a_1 = -24a1=−24

Now use the arithmetic sequence formula to find a_24a24:

a_24 = -24 + (24-1)(-3)a24=−24+(24−1)(−3)
a_24 = -24 + (23)(-3)a24=−24+(23)(−3)
a_24 = -24 -69a24=−24−69
a_24 = -93a24=−93

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