Written Instructions:
For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..
For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.
Leave your answers in the simplest form or correct to two decimal places.
| 1) Find the first five terms of the sequence given by a1 = 2, a2 = 7+a1 and an = 2an-1 + 4 for n > 2
Answer:_______________ |
| 2) Find the first five terms of the sequence given by a1 = 2, a2 = 10+a1 and an = 2an-1 + 6 for n > 2
Answer:_______________ |
| 3) Find the first five terms of the sequence given by a1 = 2, a2 = 5+a1 and an = 2an-1 + 6 for n > 2
Answer:_______________ |
| 4) Find the first five terms of the sequence given by a1 = 2, a2 = 10+a1 and an = 2an-1 + 7 for n > 2
Answer:_______________ |
| 5) Find the first five terms of the sequence given by a1 = 2, a2 = 8+a1 and an = 2an-1 + 4 for n > 2
Answer:_______________ |
| 6) Find the first five terms of the sequence given by a1 = 2, a2 = 6+a1 and an = 2an-1 + 5 for n > 2
Answer:_______________ |
| 7) Find the first five terms of the sequence given by a1 = 2, a2 = 12+a1 and an = 2an-1 + 7 for n > 2
Answer:_______________ |
| 8) Find the first five terms of the sequence given by a1 = 2, a2 = 2+a1 and an = 2an-1 + 5 for n > 2
Answer:_______________ |
| 9) Find the first five terms of the sequence given by a1 = 2, a2 = 12+a1 and an = 2an-1 + 8 for n > 2
Answer:_______________ |
| 10) Find the first five terms of the sequence given by a1 = 2, a2 = 4+a1 and an = 2an-1 + 4 for n > 2
Answer:_______________ |
| 1) Find the first five terms of the sequence given by a1 = 2, a2 = 7+a1 and an = 2an-1 + 4 for n > 2 Answer: 2,9,22,48,100 SOLUTION 1 : Given a1 = 2, a2 = 7 + a1 and an = 2an-1+4 a1 = 2 . a2 = 7 + 2 = 9 For n = 3, a3 = 2a3-1 + 4 = 2a2 + 4 = 2(9) + 4 = 22 For 4 = a4 = 2a4-1 + 4 = 2a3 + 4 = 2(22) + 4 = 48 For 5 = a5 = 2a5-1 + 4 = 2a4 + 4 = 2(48) + 4 = 100 Hence the first five terms of the sequence are 2,9,22,48,100. |
| 2) Find the first five terms of the sequence given by a1 = 2, a2 = 10+a1 and an = 2an-1 + 6 for n > 2 Answer: 2,12,30,66,138 SOLUTION 1 : Given a1 = 2, a2 = 10 + a1 and an = 2an-1+6 a1 = 2 . a2 = 10 + 2 = 12 For n = 3, a3 = 2a3-1 + 6 = 2a2 + 6 = 2(12) + 6 = 30 For 4 = a4 = 2a4-1 + 6 = 2a3 + 6 = 2(30) + 6 = 66 For 5 = a5 = 2a5-1 + 6 = 2a4 + 6 = 2(66) + 6 = 138 Hence the first five terms of the sequence are 2,12,30,66,138. |
| 3) Find the first five terms of the sequence given by a1 = 2, a2 = 5+a1 and an = 2an-1 + 6 for n > 2 Answer: 2,7,20,46,98 SOLUTION 1 : Given a1 = 2, a2 = 5 + a1 and an = 2an-1+6 a1 = 2 . a2 = 5 + 2 = 7 For n = 3, a3 = 2a3-1 + 6 = 2a2 + 6 = 2(7) + 6 = 20 For 4 = a4 = 2a4-1 + 6 = 2a3 + 6 = 2(20) + 6 = 46 For 5 = a5 = 2a5-1 + 6 = 2a4 + 6 = 2(46) + 6 = 98 Hence the first five terms of the sequence are 2,7,20,46,98. |
| 4) Find the first five terms of the sequence given by a1 = 2, a2 = 10+a1 and an = 2an-1 + 7 for n > 2 Answer: 2,12,31,69,145 SOLUTION 1 : Given a1 = 2, a2 = 10 + a1 and an = 2an-1+7 a1 = 2 . a2 = 10 + 2 = 12 For n = 3, a3 = 2a3-1 + 7 = 2a2 + 7 = 2(12) + 7 = 31 For 4 = a4 = 2a4-1 + 7 = 2a3 + 7 = 2(31) + 7 = 69 For 5 = a5 = 2a5-1 + 7 = 2a4 + 7 = 2(69) + 7 = 145 Hence the first five terms of the sequence are 2,12,31,69,145. |
| 5) Find the first five terms of the sequence given by a1 = 2, a2 = 8+a1 and an = 2an-1 + 4 for n > 2 Answer: 2,10,24,52,108 SOLUTION 1 : Given a1 = 2, a2 = 8 + a1 and an = 2an-1+4 a1 = 2 . a2 = 8 + 2 = 10 For n = 3, a3 = 2a3-1 + 4 = 2a2 + 4 = 2(10) + 4 = 24 For 4 = a4 = 2a4-1 + 4 = 2a3 + 4 = 2(24) + 4 = 52 For 5 = a5 = 2a5-1 + 4 = 2a4 + 4 = 2(52) + 4 = 108 Hence the first five terms of the sequence are 2,10,24,52,108. |
| 6) Find the first five terms of the sequence given by a1 = 2, a2 = 6+a1 and an = 2an-1 + 5 for n > 2 Answer: 2,8,21,47,99 SOLUTION 1 : Given a1 = 2, a2 = 6 + a1 and an = 2an-1+5 a1 = 2 . a2 = 6 + 2 = 8 For n = 3, a3 = 2a3-1 + 5 = 2a2 + 5 = 2(8) + 5 = 21 For 4 = a4 = 2a4-1 + 5 = 2a3 + 5 = 2(21) + 5 = 47 For 5 = a5 = 2a5-1 + 5 = 2a4 + 5 = 2(47) + 5 = 99 Hence the first five terms of the sequence are 2,8,21,47,99. |
| 7) Find the first five terms of the sequence given by a1 = 2, a2 = 12+a1 and an = 2an-1 + 7 for n > 2 Answer: 2,14,35,77,161 SOLUTION 1 : Given a1 = 2, a2 = 12 + a1 and an = 2an-1+7 a1 = 2 . a2 = 12 + 2 = 14 For n = 3, a3 = 2a3-1 + 7 = 2a2 + 7 = 2(14) + 7 = 35 For 4 = a4 = 2a4-1 + 7 = 2a3 + 7 = 2(35) + 7 = 77 For 5 = a5 = 2a5-1 + 7 = 2a4 + 7 = 2(77) + 7 = 161 Hence the first five terms of the sequence are 2,14,35,77,161. |
| 8) Find the first five terms of the sequence given by a1 = 2, a2 = 2+a1 and an = 2an-1 + 5 for n > 2 Answer: 2,4,13,31,67 SOLUTION 1 : Given a1 = 2, a2 = 2 + a1 and an = 2an-1+5 a1 = 2 . a2 = 2 + 2 = 4 For n = 3, a3 = 2a3-1 + 5 = 2a2 + 5 = 2(4) + 5 = 13 For 4 = a4 = 2a4-1 + 5 = 2a3 + 5 = 2(13) + 5 = 31 For 5 = a5 = 2a5-1 + 5 = 2a4 + 5 = 2(31) + 5 = 67 Hence the first five terms of the sequence are 2,4,13,31,67. |
| 9) Find the first five terms of the sequence given by a1 = 2, a2 = 12+a1 and an = 2an-1 + 8 for n > 2 Answer: 2,14,36,80,168 SOLUTION 1 : Given a1 = 2, a2 = 12 + a1 and an = 2an-1+8 a1 = 2 . a2 = 12 + 2 = 14 For n = 3, a3 = 2a3-1 + 8 = 2a2 + 8 = 2(14) + 8 = 36 For 4 = a4 = 2a4-1 + 8 = 2a3 + 8 = 2(36) + 8 = 80 For 5 = a5 = 2a5-1 + 8 = 2a4 + 8 = 2(80) + 8 = 168 Hence the first five terms of the sequence are 2,14,36,80,168. |
| 10) Find the first five terms of the sequence given by a1 = 2, a2 = 4+a1 and an = 2an-1 + 4 for n > 2 Answer: 2,6,16,36,76 SOLUTION 1 : Given a1 = 2, a2 = 4 + a1 and an = 2an-1+4 a1 = 2 . a2 = 4 + 2 = 6 For n = 3, a3 = 2a3-1 + 4 = 2a2 + 4 = 2(6) + 4 = 16 For 4 = a4 = 2a4-1 + 4 = 2a3 + 4 = 2(16) + 4 = 36 For 5 = a5 = 2a5-1 + 4 = 2a4 + 4 = 2(36) + 4 = 76 Hence the first five terms of the sequence are 2,6,16,36,76. |