Pedagogy of Mathematics - Part II (Numbers and Sequence - Ex 2.6), Numbers and Sequence, Maths, IX std Maths, Samacheerkalvi maths, II year B.Ed., Pedagogy, Mathematics, series, Sum to n terms of an A.P.,
28. Sum of all natural numbers between 602 and 902 which are not divisible by 4.
= Sum of all natural numbers between 602 and 902
= Sum of all natural numbers between 602 and 902 which are divisible by 4.
l = 902 – 2 = 900
To make 602 divisible by 4 we have to add 2 to 602.
∴ 602 + 2 = 604 which is divisible by 4.
To make 902 divisible by 4, subtract 2 from 902.
∴ 900 is the last number divisible by 4.
29. Sum of all natural numbers
between 602 and 902 which are
not divisible 4.
= 224848 – 56400
= 168448
33. Number of terms should be (+ve) and cannot be (-ve) or fractional number.
∴ He will take 20 months to clear the loans.
34. Answer:
Total number of steps = 30
∴ n = 30
Number of bricks for the bottom = 100
a = 100
2 bricks is less for each step
(i) Number of bricks required for the top most step
tn = a + (n – 1)d
t30 = 100 + 29 (-2)
= 100 – 58
= 42
35. (ii) Number of bricks required
Sn = n/2 [2a + (n-1) d]
S30 = 30/2 [200 + 29 (-2)]
= 15[200 – 58]
= 2130
(i) Number of bricks required for the top most step = 42 bricks
(ii) Number of bricks required = 2130