SOLUTION: the 7th term of an ap is 17 and the13th term is 12 more than the 7th term find the sum of the first 18th terms of the ap
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Question 1172506: the 7th term of an ap is 17 and the13th term is 12 more than the 7th term find the sum of the first 18th terms of the ap Found 2 solutions by Boreal, greenestamps:Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! This was shown earlier to have a1=5 and d=2 from an=a1+d(n-1)
Sum is (n/2)(2a+(n-1)d)
=(18/2)(10+2*17)=9*44=396
the terms are
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
and add to 396.
There are dozens of similar ways to solve a problem like this. Here is what I would do....
Given:
Arithmetic sequence
7th term 17
13th term 12 more than the 7th term
To find:
Sum of first 18 terms
Solution....
(1) The sum of the first 18 terms of an arithmetic sequence is 18 times the average of all the terms, which in a sequence with 18 terms is 18 times the average of the 9th and 10th terms (the two terms "in the middle").
(2) The 13th term is the 7th term plus 13-7=6 times the common difference; since the 13th term is 12 more than the 7th, the common difference is 12/6 = 2.
(3) So the 7th, 8th, 9th, and 10th terms of the sequence are 17, 19, 21, and 23.
