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Pure Mathematics
 Online Tutoring : Quiz : Pure Mathematics
Find the sum of the next 8 terms. Check your score
  Play           Question 14 of 58 in this category.    

The fourth term of an Arithmetic Progression is 8 and the sum of the first 12 terms is 126. Find the sum of the next 8 terms.
 
A.
163
B.
157
C.
160
D.
164

 
  * Quiz question created by Tutor11744 on 06 November 2005 at 12:22pm

 
 
 
 
 
 

 




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The fourth term of an Arithmetic Progression is...


formula- [(first term +last term) x #number of terms]/2=sum

let first term= f

f f+x f+2x f+3x f+4x= 8 f+5x.. f+11x (12th term)...f+19x(20thterm)

(f+f+11x)12/2=126

combine like terms to get 2f+11x=21

f+3x=8, change to f=8-3x

plug in value of  f from the second equation into the first

2(8-3x)+11x=21

solve to get x=1

solve for f now by plugging 1 into f=8-3x

f=8-3(1)  f=5

find the 20th term f+19x

=5+19(1)=24

solve for the sum of the 1st 20 with the formula to get 290

subtract the sum of the 1st 12 terms  (126) to get 164



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