Question

can you guys help me finf the first 5 terms of:

a1= 7.3
an= an-1 + 2.1

Answer 1

Answer:

a1 = 1, an = an–1 + 2, n > 1 By using the values n = 1, 2, 3, 4, 5 we can find that the first five terms. Given as a1 = 1 Now, when n = 2: a2 = a2–1 + 2 = a1 + 2 = 1 + 2 = 3 When n = 3: a3 = a3–1 + 2 = a2 + 2 = 3 + 2 = 5 When n = 4: a4 = a4–1 + 2 = a3 + 2 = 5 + 2 = 7 When n = 5: a5 = a5–1 + 2 = a4 + 2 = 7 + 2 = 9 Thus, first five terms of the sequence are 1, 3, 5, 7, 9. (ii) a1 = 1 = a2, an = an–1 + an–2, n > 2 By using the values n = 1, 2, 3, 4, 5 we can find the first five terms. Given as a1 = 1 a2 = 1 When n = 3: a3 = a3–1 + a3–2 = a2 + a1 = 1 + 1 = 2 When n = 4: a4 = a4–1 + a4–2 = a3 + a2 = 2 + 1 = 3 When n = 5: a5 = a5–1 + a5–2 = a4 + a3 = 3 + 2 = 5 Thus, first five terms of the sequence are 1, 1, 2, 3, 5. (iii) a1 = a2 =2, an = an–1 – 1, n > 2 By using the values n = 1, 2, 3, 4, 5 we can find the first five terms. Given as a1 = 2 a2 = 2 When n = 3: a3 = a3–1 – 1 = a2 – 1 = 2 – 1 = 1 When n = 4: a4 = a4–1 – 1 = a3 – 1 = 1 – 1 = 0 When n = 5: a5 = a5–1 – 1 = a4 – 1 = 0 – 1 = -1 Thus, first five terms of the sequence are 2, 2, 1, 0, -1.

2. a1 = 1 Substituting n = 2, we obtain a2 = a1 + 2 = 1 + 2 = 3 Substituting n = 3, 4 and 5, we obtain respectively a3 = a2 + 2 = 3 + 2 = 5, a4 = a3 + 2 = 5 + 2 = 7 a5 = a4 + 2 = 7 + 2 = 9 Thus, the first five terms are 1, 3, 5, 7 and 9