Question -
Answer -
(i) a1 =1, an = an–1 + 2, n > 1
By using the values n= 1, 2, 3, 4, 5 we can find the first five terms.
Given:
a1 = 1
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
∴ First five termsof 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:
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
∴ First five termsof 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:
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
∴ First five termsof the sequence are 2, 2, 1, 0, -1.