Question

Which of following is not an AP ?
a) 2,2,2,2,….
b) 10,7,4,….
c) 23,21,18,14….
d) 2,7,12,……​

Answer 1

Answer:

answer is option (c)

Step-by-step explanation:

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Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

Which of following is not an AP

a) 2,2,2,2,….

b) 10,7,4,….

c) 23,21,18,14….

d) 2,7,12,……

CONCEPT TO BE IMPLEMENTED

ARITHMETIC PROGRESSION

Arithmetic Progression ( AP ) is defined as a sequence of Real numbers such that difference between any two consecutive terms is constant

This difference is called Common Difference

EVALUATION

CHECKING FOR OPTION (a)

Here the first term = a = 2

Second Term = 2

Third Term = 2

So

Second Term - First term = 0

Third Term - Second Term = 0

$\therefore \sf{Second \: Term - First \: term = Third \: Term - Second \: Term \: }$

Hence the given numbers are in AP

CHECKING FOR OPTION (b)

Here the first term = a = 10

Second Term = 7

Third Term = 4

So

Second Term - First term = 7 - 10 = - 3

Third Term - Second Term = 4 - 7 = - 3

$\therefore \sf{Second \: Term - First \: term = Third \: Term - Second \: Term \: }$

Hence the given numbers are in AP

CHECKING FOR OPTION (c)

Here the first term = a = 23

Second Term = 21

Third Term = 18

So

Second Term - First term = 21 - 23 = - 2

Third Term - Second Term = 18 - 21 = - 3

$\therefore \sf{Second \: Term - First \: term \ne Third \: Term - Second \: Term \: }$

Hence the given numbers are not in AP

CHECKING FOR OPTION (d)

Here the first term = a = 2

Second Term = 7

Third Term = 12

So

Second Term - First term = 7 - 2 = 5

Third Term - Second Term = 12 - 7 = 5

$\therefore \sf{Second \: Term - First \: term = Third \: Term - Second \: Term \: }$

Hence the given numbers are in AP

FINAL ANSWER

The correct option is

c) 23 , 21 , 18 , 14 , ….........

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