SOLUTION: A sequence of 20 terms is formed by using f(x)=4x-1 for x=1,2,3,...,20. What is the sum of the last eight terms. i just did 20 + 19 + 18 + ... 13 and it was wrong can you please

Algebra ->  Length-and-distance -> SOLUTION: A sequence of 20 terms is formed by using f(x)=4x-1 for x=1,2,3,...,20. What is the sum of the last eight terms. i just did 20 + 19 + 18 + ... 13 and it was wrong can you please      Log On


   

Question 550252: A sequence of 20 terms is formed by using f(x)=4x-1 for x=1,2,3,...,20. What is the sum of the last eight terms.
i just did 20 + 19 + 18 + ... 13 and it was wrong can you please explain how to do it
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You are correct that the last 8 terms are
term numbers 13, 14, 15, . . . 20
+x+ = term number, and
+f%28x%29+ = the value of that term
+f%2813%29+=+4%2A13+-+1+
+f%2813%29+=+52+-+1+
+f%2813%29+=+51+
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+f%2814%29+=+4%2A14+-+1+
+f%2814%29+=+56+-+1+
+f%2814%29+=+55+
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+f%2815%29+=+4%2A15+-+1+
+f%2815%29+=+60+-+1+
+f%2815%29+=+59+
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The sum would be
4*( 13 + 14 + 15 + . . . 20 ) - (1*8)
Note that
13 + 14 + 15 + . . . 20 = sum( 1 - 20 ) - sum( 1 - 12 )
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There is a general formula for finding the sum of ( 1 - n )
For example Sum( 1 - 5 ) = 15
This is +%28n%2A%28n%2B1%29%29+%2F+2+
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Sum( 1 - 20 ) = +%2820%2A21%29%2F+2+=+210+
Sum( 1 - 12 ) = +%2812%2A13%29%2F2+=+78+
Sum ( 13 - 20 ) = +210+-+78+=+132+
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+4%2A132+=+528+
+528+-+8+=+520+
The sum of the last 8 terms is 520