SOLUTION: he 7th term of an AP is 17 and the 13th term is 12 more than the 7th term. find the first term

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Question 1172467: he 7th term of an AP is 17 and the 13th term is 12 more than the 7th term.
find the first term
Found 2 solutions by Boreal, ewatrrr:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
a7=a1+d(n-1)=a1+d(6)=17, so a1+6d=17
a13=a1+d(12), so a1+12d=29.
d=2
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a1+12=17a1=5, which is the answer.
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the difference is 2, so 6 more terms to a7 is 5+12=17


Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi  

The 7th term of an AP is 17 and the 13th term is "12 more than the 7th term". 

find the first term:

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

a%5B13%5D=29+=+a%5B1%5D+%2B+12d

+a%5B7%5D=+17+=++a%5B1%5D+%2B+6d   |Subtracting 2nd EQ from 1st EQ  eliminating a%5B1%5D

12 = 6d

red%28d=2%29

17+=+a%5B1%5D+%2B+6d |Finding a(1)

17+=+a%5B1%5D+%2B+12

green%28a%5B1%5D+=+5%29



CHECKING our answer***

29+=+a%5B1%5D+%2B+12d

29 = 5 + 24 CHECKS!!

Wish You the Best in your Studies.