Question

Which of the following is an Arithmetic Progression?
A)1,-1,-2
B)1,5,9
C)2,-2,2,-2
D)1,2,4,8​

Answer 1

we have to find out which one of the following is an Arithmetic progression.

A) 1 , -1 , -2

B) 1 , 5 , 9

C) 2 , -2 , 2 , -2

D)1 , 2, 4 , 8

solution : Arithmetic progression must have constant common difference. it means, the difference of two consecutive terms must be same.

let's check which one has constant common difference.

A) 1 , -1 , -2

difference first two terms = -1 - 1 = -2

difference of next two terms = -2 - (-1) = -2 + 1 = -1

-2 ≠ -1

so, it isn't in arithmetic progression.

B) 1, 5, 9

difference of 2nd and 1st terms = 5 - 1 = 4

difference of 3rd and 2nd terms = 9 - 5 = 4

here 2nd term - 1st term = 3rd term - 2nd term

so, it is in Arithmetic progression.

similarly, you can check other options too.

C) 2, -2 , 2, -2

-2 - 2 ≠ 2 - (-2) , so it is not in arithmetic progression.

D) 1, 2, 4 , 8

2 - 1 ≠ 4 - 2 , so it is not in arithmetic progression.

Therefore the correct option is (B) 1, 5, 9

Answer 2

Given :- Which of the following is an Arithmetic Progression ?

A)1,-1,-2

B)1,5,9

C)2,-2,2,-2

D)1,2,4,8

Solution :-

A)1,-1,-2

=> a2 - a1 = a3 - a2

=> (-1) - 1 = (-2) - (-1)

=> (-2) = (-2) + 1

=> (-2) ≠ (-1)

not an AP series .

A)1,5,9

=> a2 - a1 = a3 - a2

=> 5 - 1 = 9 - 5

=> 4 = 4

so, an AP series .

A)2,-2,2, -2

=> a2 - a1 = a3 - a2

=> (-2) - 2 = 2 - (-2)

=> (-4) ≠ 4

not an AP series .

A)1,2, 4, 8

=> a2 - a1 = a3 - a2

=> 2 - 1 = 4 - 2

=> 1 ≠ 2

not an AP series .

Hence, only (B) 1, 5, 9 is an Arithmetic Progression .

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