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

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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

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

\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}}

a_{r} > 0, r ϵ N

a_{1}

a_{2}

a_{3}

a_{2 n}

\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}}}

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

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General Form of an AP

Standard X Mathematics

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