Question

13. In an arithmetic sequence , +7. If I =-5 determine the values of I, and to show the calculations that lead to your answers 14. If x4,2x+5 and 4x + 3 represent the first three terms of an arithmetic sequence, then find the value of x. What is the fourth term? 15.18 S(1)=12 and f() = S(n-1)- 4 then which of the following represents the value of S(40)? (1) -148 (3) - 144 (2) - 140 (4) -172 16. In an arithmetic sequence of numbers a = -4 and a = 46. Which of the following is the value of a,,? (1) 120 (3) 92 (2) 146 (4) 106 17. The first term of an arithmetic sequence whose common difference is 7 and whose 22nd term is given by Q,, = 143 is which of the following? (1) -25 (3) 7 (2) -4 (4) 28

Answer 1

→ An arithmetic proguession is a sequence of numbers in which each team is derived from preceding terem by adding ou subtracting a fixed number called the common difference "d". an A.P. is To = a + (n-1)d where Tn = nth teum & a= first term de common difference - Tn - Toy th teum of m Q-13 tn = Ang +7 t i = -5 2 To find: tu & to Sol" 7 tn = tn-pt tn -tn-y = = 7 = d ( common difference) - tu a + (4-1)d -5 + (317) tu tu - 16 Ang & tro te+ (20-1) d -5 7) f 19 x 7 to = 128 Ans

2.14 Ist team x + 4 2nd twum = au +5 Jed team = 42+ 3 مس Common tr - ti difference, de = 2x+5 -x-4 di = ut 1 0 d2= t3 - tz 40+3-an - 5 dz 2x-2 2 Since common difference is same di = dz xrd an-2 ax-n- 1 + 2 x=3 Ang 4th term = tet (4-1)-d. (3+4) 3. 1 3+1) f t + 12 th 4 th team = 19

45 f(1) = 12 f(n) = f(n-1) -4 We have to find f(40) f(n) - f(n-1) --4 :d common difference) f(40) f(1) + (40-1)d 12 + 39*(-4) f/40) = -144 so option (3) is collect 16 aq = -4 a = 46 We have to find a 12 ao al + (6-1)d > 46 -4 + 5d 50 = 5d d = 10 ajz (12-1)d Art -4 + 11x10 A12= 106 Ang So option (4) is conuect

17 Common difference, d= 7 A22 143 We have to find a Sol? A22 = A + (22-1) d 143 al + 21*7 143 147 = all A =-4 So option (2) is couiect