Question

13. The sum of five consecutive odd numbers is 685. What are the
numbers.
14.If Sn denotes the sum of n terms of an AP whose common difference is
'd' and first term is 'a'. Find Sn - 2Sn-1 +Sn-2
15. Find x if (8x + 4), (6x – 2) and (2x + 7) are in AP.​

Answer 1

Ans 13 :

Let the odd consecutive numbers be x , x + 2 , x + 4 , x + 6 and x + 8 .

ATQ :

x + x + 2 + x + 4 + x + 6 + x + 8 = 685

5x + 20 = 685

5x = 685 - 20

x = 665 / 5 = 133

First number = x = 133

Second number = x + 2 = 135

Third number = x + 4 = 137

Fourth number = x + 6 = 139

Fifth number = x + 8 = 141

Ans 14 :

First term = a

Common difference = d

Sum of n terms = Sₙ

We know that :

aₙ = Sₙ - Sₙ₋₁

And ,

aₙ₋₁ = Sₙ₋₁ - Sₙ₋₂

To find :

Sₙ - 2Sₙ₋₁ + Sₙ₋₂

= Sₙ - Sₙ₋₁ - Sₙ₋₁ + Sₙ₋₂

= (Sₙ - Sₙ₋₁) - (Sₙ₋₁ - Sₙ₋₂)

= aₙ - aₙ₋₁

= d

Ans 15 :

AP : (8x + 4) , (6x - 2) , (2x + 7)

d = (6x - 2) - (8x + 4) _____(i)

Also ,

d = (2x + 7) - (6x - 2) ____(ii)

Equating (i) and (ii) equations :

(6x - 2) - (8x + 4) = (2x + 7) - (6x - 2)

6x - 8x - 2 - 4 = 2x - 6x + 7 + 2

-2x - 6 = -4x + 9

2x = 15

x = 15/2