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Prove that am + n + am - n =2am
Ans: a m + n = a1 + (m + n - 1) d
a m-n = a1 + (m - n -1) d
am = a1 + (m-1) d
Add 1 & 2
a m+n + a m-n = a1+(m+n-1) d+ a1 + (m-n-1)d
= 2a1+(m+n+m-n-1-1)d
= 2a1+ 2(m-1)d
= 2[a1+ (m-1)d]
= 2am. Hence proved.
x+2y^2=63 and 4x+y^2=0; Find the area of the regions enclosed by the lines and curves.
275/41
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Consider the system of linear equations X + ay = 1 2x + 8y = b Where a and b are real numbers. (a) Write out the augmented matrix for this system of linear equations.
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