Question

7. Find the next two terms of each geometric sequence. a.-3.9. - 27. 81.... b. I. -1.1.-1.1. - 1.... 8. Find the first five terms of the geometric sequence for which ,- -2 and 3. 9. Find , for the geometric sequence 60, 30, 15.... 10. Write an equation for the nth term of the geometric sequence 4, 8, 16,... 11. The second term in a geometric sequence is -2 and the third term is-6. Find an equation for the nth term of this sequence? 12. Generate the next three terms of each arithmetic sequence shown below. (a) a = -2 and d =4 (b) S (n)=f(n-1)-8 with (1)=10 (c) a = 3, a, = 1

Answer 1

(7)(a) Given geometric sequence -3, 9, -27, 81, Нос loand first torm a = -3 common ratio ta - 27 .-3 81 -27 واله ( ) -3 81 Will we ท-) Here foufith form is i ty=81 We find to, to know that fn = an -3 x(3)!= -3*81 -243 and for a (-3) (-3)^-'=63)(-3) = .38243 = 729 two terms - 243, 729 t5 (-3)* 6-3,5-) Here last 1,-1, 1,-1, 1,-1 Here first form as 1 common ratio na aj Нелс We We find tq and to know that tn= annel 1*(-17-2 & t7 - and tg = 18.-198-1 =1*(-1)7 Hence last two forms [1,1]

© Given 013-2 and = 3 WC n-1 know that an= ann Hore a=a = -2 aza -2*(332-'- - 2*3 2-6 a3 6-2)*(3)3-1 ay6-2)(394-'. -2*97 = -54 62)x (3)5-) -2x342 -2x81 2-162 - -2x92-18 ag Hence first tive forms 4TIt -2, -6, -18, -54,-162 ♡) Given sequence 60, 36,15 Horr first form a common satio ha 30 --- / we know n th Home&ric serion sequence that Form an apni n-1 Gox(?)" 29-1 = Gox 2 anti - 6002 2 2 2 = 120x2 Hence an = 120x2n (10) Given geometric sequence 4, 8, 16. Here first form a=4 common ratio (b) / = 16 = met 2 We know that nth form of a Jeometric sequence 4x(2) ) anzanne 4*2 = 2x29 Hence an 294) 2274)

(1) onth form sequence in a Feometric that We know an= anny (A) Given 92= -2 ar = -2 (1) and az=-6 ant= -6 - (2) NOW ash from (1) and (2) anh -L +2 an → ha 3 from (1) a=-2 / Hence the prom (A) Sequence - B --26 countion on th term of of this (-23)*(3) -) 2 -2 * 3 -1-) n22 2x39-21 ana Hence an=

a) Giren a = -2 and d=4 WC know that in a arithmetic sequence an = at(n-1) d Given 91-9--2 and d=4 a2s – 2+ (2-1) 4 2 - 2 + 4 = 2 az = = 6 - 2 + (3-1) 4 -2+8 an = -2+(1-1)52-2+12 10 Hence next three houree terms 2, 6, 10 (6) Given f(n)= f(n-1) -8 and f(1) = 10 Then H2) = H2-1)-8=71-8 310-8=2 413) = H3-1)-8 = +(2)-8 = 2-8 = -6 = 413) -8 =-6-8--14 +14) f(4-1) -8 2,-6, 14 Hence next three terns 16) Given 91 = 3, 9221 Then common di Herence d = a2-a = 1-3 = -2 we know an = at(n-1)d C'9=91-3) 3+ (3-1)(-2) = 3-4-1 43 - ay= 3+ (4-1) (-2) = 3-62-3 as 3+ (5-1) (-2) = 3-82-5 -1, -3,-5 Hence last three forms