the sum of 3rd and 7th term of an ap is 6 and their product is 8 find the sum of first 18 terms
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a3+a7=6
a+2d+a+6d=6
2a+8d=6
Taking 2 common
a+4d=3
a=3-4d...(1)
Product is 8
(a+2d)(a+6d)=8
Putting value of 'a'
(3-4d+2d)(3-4d+6d)=8
(3-2d)(3+2d)=8
3^2-2d^2=8
9-4d^2=8
-4d^2=-1
d^2=1/2...(2)
Use EQ.2 in 1 we get
a=1
To calculate the sum of 18 terms
Using formula
N/2(2a+(n-1)d
18/2(2*1+(18-1)*1/2
9(2+17/2)
9*(4+17/2)
9*21/2
189/2
94.5 is the answer
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