Question

What is the next number in the series 70,54,45,41?

a. 40

b. 35

c. 45

d. 54?

Answer 1

a. 40

because no. are decreasing in squares
$that \: is \: 70 - {4}^{2} = 70 - 16 = 54 \\ \\ now \: 54 - {3}^{2} = 54 - 9 = 45 \\ \\ now \: 45 - {2}^{2} = 45 - 4 = 41 \\ \\ so \: 41 - {1}^{2} = 40 - 1 = 40$

Answer 2

Answer:  The correct option is (a) 40.

Step-by-step explanation:  We are given to select the next number in the following series :

70,  54,  45,  41,  .  .  .

Let a(n) denote the n-th term of the given series.

Then, we observe that

$a(1)=70,\\\\a(2)=54=70-16=a(1)-4^2,\\\\a(3)=45=54-9=a(2)-3^2,\\\\a(4)=41=45-4=a(3)-2^2,\cdots$

Repeating the above rule, we get

$a(5)=a(4)-1^2=41-1=40.$

Thus, the next term in the given series is 40.

Option (a) is CORRECT.