(i) The sum of the first n terms of an AP is `((5n^(2))/(2) + (3n)/(2))`. Find the nth term and the 20th term of this AP. (ii) The sum of the first n

Correct Answer - C `(c )` Let the first term be `a` and the common difference `d`. Then it is given that `a+8d=55` and ……..`(i)` `1900 lt (25)/(2)(2a+24d) lt 2000` `:.1900...

Correct Answer - D `(d)` `x_(1)+x_(2)+x_(3)+……+x_(100)=(100)/(2)(x_(1)+x_(100))=-1` `impliesx_(1)+x_(100)=-(1)/(50)` `x_(2)+x_(4)+…+x_(100)=(50)/(2)(x_(1)+d+x_(100))=1` `impliesx_(1)+x_(100)+d=(1)/(25)` `impliesd=(3)/(50)` ltbr `x_(1)+x_(1)+99d=(-1)/(50)` `impliesx_(1)=(-149)/(50)` `x_(100)=x_(1)+99d` `=(-149)/(50)+99xx(3)/(50)` `=(74)/(25)`

Correct answer is (C) -90 

Correct Answer - `+n xx L.C. `

Correct Answer - `3/2(1-1/3^(n))`

Correct Answer - `(1)/(2)n(n+1)(2n+3)`

Correct Answer - `n(n+1)^(2)(n+2)`

Correct Answer - (i) 85 (ii) -82 (iii) `35sqrt(2) (iv) 4(3)/(4)` (v) 310

Correct Answer - (i) 893 (ii) -56 (iii) - 80 (iv) `(33)/(20)` (v) 5505

First Term of the AP (a) = 5 Common difference (d) = 8 - 5 = 3 Last term = a40 = a + (40 - 1) d = 5 + 39 × 3...