Question 2Justify whether it is true to say that-1- -3-2-2- 5-2- - forms an AP as a2 -a1 - a3 -a2-

Here, a_1= 1, a_2= 3/2, a_3= 2 and a_4=5/2 a_2 a_1 = 3/1+1= 1/2 a_3 a_2 = 2+3/2= 1/2 a_4 a_3 =5/2+2 =9/2 Clearly, the difference between successive terms i ...

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Quantitative Aptitude

Divisibility Rule for Powers of 2 & 5

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Question 2
Justify whether it is true to say that
$- 1, \frac{- 3}{2}, - 2, \frac{5}{2}, \dots$
forms an AP as $a_{2} - a_{1} = a_{3} - a_{2}$ .

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Solution

$H e r e, a_{1} = - 1, a_{2} = \frac{- 3}{2}, a_{3} = - 2 a n d a_{4} = \frac{5}{2}$
$a_{2} - a_{1} = \frac{- 3}{1} + 1 = - \frac{1}{2}$
$a_{3} - a_{2} = - 2 + \frac{3}{2} = - \frac{1}{2}$
$a_{4} - a_{3} = \frac{5}{2} + 2 = \frac{9}{2}$

Clearly, the difference between successive terms is not the same for all.
Therefore, the terms do not form an AP.

Hence, the given statement is false.

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Similar questions

Q. Question 2
Justify whether it is true to say that

- 1, \frac{- 3}{2}, - 2, \frac{5}{2}, \dots

forms an AP as

a_{2} - a_{1} = a_{3} - a_{2}

Q. Justify whether it is true to say that

- 1, - \frac{3}{2}, - 2, \frac{5}{2}, . . .

,... forms an AP as

a_{2} a_{1} = a_{3} a_{2}

.
If true then enter

1

and if false then enter

0

Q. Question 23
If

a_{n} = 3 - 4 n

, then show that

a_{1}, a_{2}, a_{3}, \dots

form an AP. Also, find

S_{20}

Q. Show that

\frac{a_{1}}{a_{1}} + \frac{a_{2}}{a_{2}} + \frac{a_{3}}{a_{3}} + \dots \frac{a_{n}}{a_{n}} = \frac{1}{1} + \frac{1}{a_{1}} + \frac{a_{1}}{a_{2}} + \frac{a_{2}}{a_{3}} + \dots \frac{a_{n - 2}}{a_{n - 1}}

Q. If

a_{r} > 0, r ϵ N

and

a_{1}

a_{2}

a_{3}

,...,

a_{2 n}

are in AP then

\frac{a_{1} + a_{2 n}}{\sqrt{a_{1}} + \sqrt{a_{2}}} + \frac{a_{2} + a_{2 n - 1}}{\sqrt{a_{2}} + \sqrt{a_{3}}} + \frac{a_{3} + a_{2 n - 2}}{\sqrt{a_{3}} + \sqrt{a_{4}}} + . . . + \frac{a_{n} + a_{n + 1}}{\sqrt{a_{n}} + \sqrt{a_{n + 1}}}

is equal to

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Divisibility Rule for Powers of 2 & 5

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Question 2 Justify whether it is true to say that −1,−32,−2,52, ⋯ forms an AP as a2−a1=a3−a2.

Here, a1=−1, a2=−32, a3=−2 and a4=52 a2−a1=−31+1=−12 a3−a2=−2+32=−12 a4−a3=52+2=92 Clearly, the difference between successive terms is not the same for all. Therefore, the terms do not form an AP. Hence, the given statement is false.

Question 2
Justify whether it is true to say that
$- 1, \frac{- 3}{2}, - 2, \frac{5}{2}, \dots$
forms an AP as $a_{2} - a_{1} = a_{3} - a_{2}$ .