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 = 15+a1 and an = 2an-1 + 5 for n > 2
Answer:_______________ |
| 2) Find the first five terms of the sequence given by a1 = 2, a2 = 2+a1 and an = 2an-1 + 6 for n > 2
Answer:_______________ |
| 3) Find the first five terms of the sequence given by a1 = 2, a2 = 2+a1 and an = 2an-1 + 5 for n > 2
Answer:_______________ |
| 4) Find the first five terms of the sequence given by a1 = 2, a2 = 8+a1 and an = 2an-1 + 5 for n > 2
Answer:_______________ |
| 5) Find the first five terms of the sequence given by a1 = 2, a2 = 12+a1 and an = 2an-1 + 5 for n > 2
Answer:_______________ |
| 6) Find the first five terms of the sequence given by a1 = 2, a2 = 3+a1 and an = 2an-1 + 8 for n > 2
Answer:_______________ |
| 7) Find the first five terms of the sequence given by a1 = 2, a2 = 14+a1 and an = 2an-1 + 4 for n > 2
Answer:_______________ |
| 8) Find the first five terms of the sequence given by a1 = 2, a2 = 7+a1 and an = 2an-1 + 5 for n > 2
Answer:_______________ |
| 9) Find the first five terms of the sequence given by a1 = 2, a2 = 14+a1 and an = 2an-1 + 6 for n > 2
Answer:_______________ |
| 10) Find the first five terms of the sequence given by a1 = 2, a2 = 4+a1 and an = 2an-1 + 6 for n > 2
Answer:_______________ |
| 1) Find the first five terms of the sequence given by a1 = 2, a2 = 15+a1 and an = 2an-1 + 5 for n > 2 Answer: 2,17,39,83,171 SOLUTION 1 : Given a1 = 2, a2 = 15 + a1 and an = 2an-1+5 a1 = 2 . a2 = 15 + 2 = 17 For n = 3, a3 = 2a3-1 + 5 = 2a2 + 5 = 2(17) + 5 = 39 For 4 = a4 = 2a4-1 + 5 = 2a3 + 5 = 2(39) + 5 = 83 For 5 = a5 = 2a5-1 + 5 = 2a4 + 5 = 2(83) + 5 = 171 Hence the first five terms of the sequence are 2,17,39,83,171. |
| 2) Find the first five terms of the sequence given by a1 = 2, a2 = 2+a1 and an = 2an-1 + 6 for n > 2 Answer: 2,4,14,34,74 SOLUTION 1 : Given a1 = 2, a2 = 2 + a1 and an = 2an-1+6 a1 = 2 . a2 = 2 + 2 = 4 For n = 3, a3 = 2a3-1 + 6 = 2a2 + 6 = 2(4) + 6 = 14 For 4 = a4 = 2a4-1 + 6 = 2a3 + 6 = 2(14) + 6 = 34 For 5 = a5 = 2a5-1 + 6 = 2a4 + 6 = 2(34) + 6 = 74 Hence the first five terms of the sequence are 2,4,14,34,74. |
| 3) 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. |
| 4) Find the first five terms of the sequence given by a1 = 2, a2 = 8+a1 and an = 2an-1 + 5 for n > 2 Answer: 2,10,25,55,115 SOLUTION 1 : Given a1 = 2, a2 = 8 + a1 and an = 2an-1+5 a1 = 2 . a2 = 8 + 2 = 10 For n = 3, a3 = 2a3-1 + 5 = 2a2 + 5 = 2(10) + 5 = 25 For 4 = a4 = 2a4-1 + 5 = 2a3 + 5 = 2(25) + 5 = 55 For 5 = a5 = 2a5-1 + 5 = 2a4 + 5 = 2(55) + 5 = 115 Hence the first five terms of the sequence are 2,10,25,55,115. |
| 5) Find the first five terms of the sequence given by a1 = 2, a2 = 12+a1 and an = 2an-1 + 5 for n > 2 Answer: 2,14,33,71,147 SOLUTION 1 : Given a1 = 2, a2 = 12 + a1 and an = 2an-1+5 a1 = 2 . a2 = 12 + 2 = 14 For n = 3, a3 = 2a3-1 + 5 = 2a2 + 5 = 2(14) + 5 = 33 For 4 = a4 = 2a4-1 + 5 = 2a3 + 5 = 2(33) + 5 = 71 For 5 = a5 = 2a5-1 + 5 = 2a4 + 5 = 2(71) + 5 = 147 Hence the first five terms of the sequence are 2,14,33,71,147. |
| 6) Find the first five terms of the sequence given by a1 = 2, a2 = 3+a1 and an = 2an-1 + 8 for n > 2 Answer: 2,5,18,44,96 SOLUTION 1 : Given a1 = 2, a2 = 3 + a1 and an = 2an-1+8 a1 = 2 . a2 = 3 + 2 = 5 For n = 3, a3 = 2a3-1 + 8 = 2a2 + 8 = 2(5) + 8 = 18 For 4 = a4 = 2a4-1 + 8 = 2a3 + 8 = 2(18) + 8 = 44 For 5 = a5 = 2a5-1 + 8 = 2a4 + 8 = 2(44) + 8 = 96 Hence the first five terms of the sequence are 2,5,18,44,96. |
| 7) Find the first five terms of the sequence given by a1 = 2, a2 = 14+a1 and an = 2an-1 + 4 for n > 2 Answer: 2,16,36,76,156 SOLUTION 1 : Given a1 = 2, a2 = 14 + a1 and an = 2an-1+4 a1 = 2 . a2 = 14 + 2 = 16 For n = 3, a3 = 2a3-1 + 4 = 2a2 + 4 = 2(16) + 4 = 36 For 4 = a4 = 2a4-1 + 4 = 2a3 + 4 = 2(36) + 4 = 76 For 5 = a5 = 2a5-1 + 4 = 2a4 + 4 = 2(76) + 4 = 156 Hence the first five terms of the sequence are 2,16,36,76,156. |
| 8) Find the first five terms of the sequence given by a1 = 2, a2 = 7+a1 and an = 2an-1 + 5 for n > 2 Answer: 2,9,23,51,107 SOLUTION 1 : Given a1 = 2, a2 = 7 + a1 and an = 2an-1+5 a1 = 2 . a2 = 7 + 2 = 9 For n = 3, a3 = 2a3-1 + 5 = 2a2 + 5 = 2(9) + 5 = 23 For 4 = a4 = 2a4-1 + 5 = 2a3 + 5 = 2(23) + 5 = 51 For 5 = a5 = 2a5-1 + 5 = 2a4 + 5 = 2(51) + 5 = 107 Hence the first five terms of the sequence are 2,9,23,51,107. |
| 9) Find the first five terms of the sequence given by a1 = 2, a2 = 14+a1 and an = 2an-1 + 6 for n > 2 Answer: 2,16,38,82,170 SOLUTION 1 : Given a1 = 2, a2 = 14 + a1 and an = 2an-1+6 a1 = 2 . a2 = 14 + 2 = 16 For n = 3, a3 = 2a3-1 + 6 = 2a2 + 6 = 2(16) + 6 = 38 For 4 = a4 = 2a4-1 + 6 = 2a3 + 6 = 2(38) + 6 = 82 For 5 = a5 = 2a5-1 + 6 = 2a4 + 6 = 2(82) + 6 = 170 Hence the first five terms of the sequence are 2,16,38,82,170. |
| 10) Find the first five terms of the sequence given by a1 = 2, a2 = 4+a1 and an = 2an-1 + 6 for n > 2 Answer: 2,6,18,42,90 SOLUTION 1 : Given a1 = 2, a2 = 4 + a1 and an = 2an-1+6 a1 = 2 . a2 = 4 + 2 = 6 For n = 3, a3 = 2a3-1 + 6 = 2a2 + 6 = 2(6) + 6 = 18 For 4 = a4 = 2a4-1 + 6 = 2a3 + 6 = 2(18) + 6 = 42 For 5 = a5 = 2a5-1 + 6 = 2a4 + 6 = 2(42) + 6 = 90 Hence the first five terms of the sequence are 2,6,18,42,90. |