SOLUTION: For an arithmetic sequence a<sub>13</sub> = 241 and common difference = 7. Determine the explicit formula and the first five terms of the sequence

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Question 1103995: For an arithmetic sequence a13 = 241 and common difference = 7. Determine the explicit formula and the first five terms of the sequence
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

a%5Bn%5D%22%22=%22%22a%5B1%5D%2B%28n-1%29d

Substitute n = 13, d = 7

a%5B13%5D%22%22=%22%22a%5B1%5D%2B%2813-1%29%287%29

a%5B13%5D%22%22=%22%22a%5B1%5D%2B%2812%29%287%29

a%5B13%5D%22%22=%22%22a%5B1%5D%2B84

Substitute a13 = 241

241%22%22=%22%22a%5B1%5D%2B84

Subtract 84 from both sides

157%22%22=%22%22a%5B1%5D

Back to

a%5Bn%5D%22%22=%22%22a%5B1%5D%2B%28n-1%29d

Substitute a1 = 157, d = 7

a%5Bn%5D%22%22=%22%22157%2B%28n-1%29%287%29

a%5Bn%5D%22%22=%22%22157%2B7%28n-1%29

a%5Bn%5D%22%22=%22%22157%2B7n-7

a%5Bn%5D%22%22=%22%227n%2B150 <--explicit formula

To find first five terms, write first term 157, and
add 7 successively to it and each preceding term to get the
next term:

157, 164, 171, 178, 185  <--first five terms

Edwin