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

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 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard X

Mathematics

General Form of an AP

Question 2 Ju...

Question

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

Open in App

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.

Suggest Corrections

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. 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

Q. Question 8 (i)
Justify whether it is true to say that the following are the nth terms of an AP.
2n – 3

Join BYJU'S Learning Program

Explore more

General Form of an AP

Standard X Mathematics

Join BYJU'S Learning Program

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