Answer:
(i)
Arithmetic Progression (AP) whose common difference is = an – an-1 where n > 0
Consider,
a = a1 = 1, a2 = 4 …
Common difference, d = a2 – a1 = 4 – 1 = 3
Finding an
an = a + (n-1) d
= 1 + (n-1) 3
= 1 + 3n – 3
= 3n – 2
When n = 10,
a10 = 3(10) – 2
= 30 – 2
= 28
10th term is 28.
(ii)
Arithmetic Progression (AP) whose common difference is = an – an-1 where n > 0
Consider,
a = a1 = √2, a2 = 3√2 …
Common difference, d = a2 – a1 = 3√2 – √2 = 2√2
Find an
an = a + (n-1) d
= √2 + (n – 1) 2√2
= √2 + 2√2n – 2√2
= 2√2n – √2
When n = 18,
a18 = 2√2(18) – √2
= 36√2 – √2
= 35√2
10th term is 35√2