Question

solve this -1,1,-2,2,-3,3,-4,4 is A.p or not

Answer 1

$a 1 = - 1 \\ a2 = 1 \\ a3 = - 2 \\ a4 = 2 \\ a5= - 3 \\ a6 = 3 \\ a7 = - 4 \\ a8 = 4 \\ a2 - a1 = 1 - ( - 1) = 2 \\ a3 - a2 = - 2 - 1 = - 3 \\ since \: a3 - a2not \: equal \: to \: a2 - a1 \\ therefore \: the \: series \: is \: not \: in \: ap$
hope it will help you

Answer 2

A.P is the acronym for Arithmetic Progeression.

• A sequence is called is called an arithmetic progression only if the common difference(d) is same.

• I.e $\large\mathbf{If \: a_1, a_2, a_3, ..... \: is \: an \: A.P \: then,} \\ \mathbf{a_1 = -1; a_2 = 1; a_3 = -2; a_4 = 2...}$

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$\large\mathbf{a_2 - a_1 = a_3 - a_2 }$

Checking the values,

$\large\mathbf{a_2 - a_1 = a_3 - a_2}$

$\large\mathbf{=> 1 - (-1) = -2 - 1}$

$\large\mathbf{=> 1+1 = -3}\\\large\mathbf{=> 2 = -3}\\\\\textbf{This is a False Statement.}$

$\textbf{There is no common difference(d).}\\ \textbf{Hence, the given sequence is not an A.P}$

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