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Mathematics, , (Chapter — 5) (Arithmetic Progressions), (Class - X), , Exercise 5.3, , Question 1:, , Find the sum of the following APs., (i) 2, 7, 12,...., to 10 terms., , (ii) — 37, -— 33, - 29 ,..., to 12 terms, (iii) 0.6, 1.7, 2.8 ,........, to 100 terms, , a4, (iV) SB espeagenns to 11 terms, , Answer 1:, , (i) 2, 7, 12 ,..., to 10 terms, , For this A.P., a = 2,d =a2- a1=7-2=S5andn=10, We know that,, , §, =5[2a+(n-1)4], $= 2[2(2)+(10-1)5], , = 5[4+(9)x(5)], = 5x49 = 245, , (ii) -37, -33, -29 ,..., to 12 terms, , For this A.P., a = —37, d = a2 — a; = (—33) — (-37) = —- 33+ 37 = 4, n=12, , We know that,

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Ss, =F [22+(n-1)4], , 5, *= (2(-37)+(12-1)4], =6[-74+11x4], =6[-74+44], = 6(-30) = -180, , (iii) 0.6, 1.7, 2.8 ,..., to 100 terms, For this A.P., a = 0.6, d = a2 — a1 = 1.7 —-0.6 = 1.1 andn = 100, We know that,, , n, S, =5l24+(n-1)4), , a = 10°F 2(0.6)+(100-1)1.1], = 50[1.2+(99)x(1.1)], = 50[1.2+108.9], = S0[110.1}, = 5505, , (iv) =,4,5,....., to 11 terms, , For this A.P.,, 1, a=—, 1s, n=i1, 14, d=a,-a,*—-—, ale, 1, 60 «60

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We know that,, , Find the sums given below, (i) 7 + 105 + 14 + crecssoe + 84, , (ii) 34 + 32 + 30 + cesaeee +10, , (iii) - 5 + (-— 8) + (- 11) + ww * (— 230), , , , Answer 2:, (i) 7 + 105 + 14 + erent 84, For this A.P.,, , a=7and /= 84, , dxaj-a,ni01-7utl7 0!, ea 9, , Let 84 be the n™ term of this A.P., l=a+(n-1)d

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84=7+(n-1)2, , 7=(n-1)2, , 22=n-1, n= 23, , We know that,, S,=F(a+!), x = Bir +84], , _ 23x91 _ 2093, , , , , , (ii)34 + 32 + 30 + ... +10, For this A.P., a = 34, d = a2 — a1 = 32 — 34 = -2 and/=10, Let 10 be the n™ term of this A.P./=a+(n-1)d, , 10 = 34 + (n — 1) (—2), -24 = (nm — 1) (-2), 12=n-1, , n=13, , S, =F(a+l), , 13, ==(34+10, , 7 (34+10), _ 13x44, , , , = 13x22, = 286

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(iii)(—5) + (-B) + (-11) + cnecssce + (-230), , For this A.P.,, a = —5,/ = —230 and d = a2 — a; = (-8) —- (-5) = -8+5=-3, Let —230 be the n® term of this A.P., , l=a+(n-1)d, , -230 = — 5 + (n —- 1) (-3), -225 = (n — 1) (-3), (n-1)=75, , n= 76, , And, S,= 5(a+!), , - 2 [(-s)+(230)], , = 38(-235), =-8930, , Question 3:, In an AP, , (i) Given a = 5, d = 3, an = 50, find n and Sn., , (ii) Given a = 7, a;3 = 35, find d and Sy3., , (iii) Given a2 = 37, d = 3, find a and Siz., , (iv) Given a3 = 15, Sic = 125, find d and aio., , (v) Given d = 5, Ss = 75, find a and as., , (vi) Given a = 2, d = 8, Sn = 90, find n and an., , (vii) Given a = 8, a. = 62, Sp, = 210, find n and d., , (viii) Given a, = 4, d = 2, Sn = — 14, find n and a., , (ix) Given a = 3, n= 8, S = 192, find d., , (x)Given / = 28, S = 144 and there are total 9 terms. Find a.