Answers:

(i)

First term, a = a₁ = 2

Common difference, d = a₂ – a₁ = 5 – 2 = 3

a_n term of given AP is 182

a_n = a + (n-1) d

182 = 2 + (n-1) 3

182 = 2 + 3n – 3

182 = 3n – 1

3n = 182 + 1

n = 183/3

n = 61

By using the formula,

S = n/2 (a + l)

S = 61/2 (2 + 182)

S = 61/2 (184)

S = 61 (92)

S = 5612

∴ The sum of the series is 5612

(ii) 

First term, a = a₁ = 101

Common difference, d = a₂ – a₁ = 99 – 101 = -2

a_n term of given AP is 47

a_n = a + (n-1) d

47 = 101 + (n-1)(-2)

47 = 101 – 2n + 2

2n = 103 – 47

2n = 56

n = 56/2 = 28

S = n/2 (a + l)

S = 28/2 (101 + 47)

S = 28/2 (148)

S = 14 (148)

S = 2072

∴ The sum of the series is 2072