Question

A) write the half of natural numbers as a sequence
b) write the integers in that sequence in order.
c) what will be the position of number 23 in
the first sequence ?
d) find the sum of the first fifty terms
of the first sequence,​

Answer 1

Solution:

(a)

• The sequence for half of natural numbers is given by

• 1/2, 1, 3/2, 2, 5/2, 3, 7/2, 4, 9/2, 5, 11/2, 6, 13/2, 7, ...

(b)

• The integers in order are given by

• 1, 2, 3, 4, 5, 6, 7, ...

(c)

• The first sequence is

• 1/2, 1, 3/2, 2, 5/2, 3, 7/2, 4, 9/2, 5, 11/2, 6, 13/2, 7, ...

• First term = 1/2

• Common difference = 1/2

• Let 23 be the nth term in the sequence.

• Then, 1/2 + (n - 1) * 1/2 = 23

• or, 1/2 * (1 + n - 1) = 23

• or, n = 46

• So 23 is the 46th term in the sequence.

(d)

• The first sequence is

• 1/2, 1, 3/2, 2, 5/2, 3, 7/2, 4, 9/2, 5, 11/2, 6, 13/2, 7, ...

• First term = 1/2

• Common difference = 1/2

• So 50th term = 1/2 + (50 - 1) * 1/2

• = 1/2 + 49/2

• = (1 + 49)/2

• = 50/2

• = 25

• Thus sum of the first fifty terms is

• = 50/2 * (first term + 50th term)

• = 25 * (1/2 + 25)

• = 25 * 51/2

• = 637.5