In an A.P:
(i) Given `a= 5, d=3, a_(n) = 50`, find n and `S_(n)`.
(ii) Given `a=7, a_(13) = 35`, find 'd' and `S_(13)`.
(iii) Given `a_(12) = 37 , d=3`, find a and `S_(12)`.
(iv) Given `a_(3) = 15, S_(10) = 125`, find 'd' and `a_(10)`.
(v) Given `d= 5, S_(9) = 75`, find 'a' and `a_(9)`.
(vi) Given `a=2, d=8, S_(n) = 90`, find 'n' and `a_(n)`.
(vii) Given `a=8, I=a_(n) = 62,S_(n) = 210`, find 'n' and 'd'.
(viii) Given `a_(n) = 4=I, d=2, S_(n) = -14`, find 'n' and 'a'.
(ix) Given `a=3, n=8, S_(n)= 192`, find 'd'.
(x) Given `I= 28, S_(n) = 144`, and there are a total 9 terms find 'a' .

Answer

(i) `S_(16) = (16)/(2) [ 5+ 50] =8 xx 55 = 440`
(ii) `S_(13) = (13)/(2) [ 7+35] = (13)/(2) xx 42 = 13 x 21 = 273`
(iii) `S_(12) = (12)/(2) [ 4+ 37] = 6 xx 41 = 246`
(iv) `a_(10) = a+9d = (a+2d) + 7d = 15+ 7(-1) = 15-7 =8`
(v) `= (-35)/(3) + (8 xx 5) = (-35)/(3) + 40 rArr (-35 + 120)/(3) = (85)/(3)`.
(vii) `a_(5) = 2+ (5-1) 8=2 + 32 = 34`.
(viii) `d=(54)/(5)`
(viii) We have, `a=6 -2n =6 -2 (7) = 6 -14 = -8`.
(ix) `d=(42)/(7) =6`
(x) `a=32-28=4`