Answers:
(i)
n = 25
First term, a = a1 = 3
Common difference, d = a2 – a1 = 9/2 – 3 = (9 – 6)/2 = 3/2
By using the formula,
S = n/2 (2a + (n – 1) d)
Substitute the values of ‘a’ and ‘d’, we get
S = 25/2 (2(3) + (25-1) (3/2))
S = 25/2 (6 + (24) (3/2))
S = 25/2 (6 + 36)
S = 25/2 (42)
S = 25 (21)
S = 525
∴ The sum of the given AP is 525.
(ii)
n = 12
First term, a = a1 = 41
Common difference, d = a2 – a1 = 36 – 41 = -5
By using the formula,
S = n/2 (2a + (n – 1) d)
Substitute the values of ‘a’ and ‘d’, we get
S = 12/2 (2(41) + (12-1) (-5))
S = 6 (82 + (11) (-5))
S = 6 (82 – 55)
S = 6 (27)
S = 162
∴ The sum of the given AP is 162.