Question

Sum of 3rd & 7th terms of an ap is 6 and thier product is 8 find the sum of 1st 17 terms of the ap

Answer 1

Case (a): d= 0.5 

a+4d = 3==> a=3-4d = 3-4(0.5)=1 

3rd term = a+2d= 1+2*0.5 = 2 

7th term = a+6d= 1+6*0.5 = 4 

Sum = 6 and Product = 8 

Case (b): d= -0.5 

a+4d = 3==> a=3-4d = 3-4(-0.5) = 3+2 = 5 

3rd term = a+2d= 5+2*(-0.5) = 4 

7th term = a+6d= 5+6*(-0.5) = 2 

Sum = 6 and Product = 8 

Since both are matching, we will go with bothvalues

Sum of first 16 terms = n*(2a+(n-1)d)/2 = 16*(2a+15d)/2 

= 8*(2a+15d) 

Case (a): d= 0.5 

Sum = 8*(2*1+15*0.5)=76 

Case (b): d= 0.5 

Sum = 8*(2*5+15*(-0.5))=20