Justify whether it is true to say that -1, -f | vedclass

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(B) False.Here,$a_{1} = -1, a_{2} = -\frac{3}{2}, a_{3} = -2$ and $a_{4} = \frac{5}{2}$.Calculate the common differences:$a_{2} - a_{1} = -\frac{3}{2}

Vedclass · Accepted Answer

False

Vedclass · Answer

(B) False.Here,$a_{1} = -1, a_{2} = -\frac{3}{2}, a_{3} = -2$ and $a_{4} = \frac{5}{2}$.Calculate the common differences:$a_{2} - a_{1} = -\frac{3}{2} - (-1) = -\frac{3}{2} + 1 = -\frac{1}{2}$.$a_{3} - a_{2} = -2 - (-\frac{3}{2}) = -2 + \frac{3}{2} = -\frac{1}{2}$.$a_{4} - a_{3} = \frac{5}{2} - (-2) = \frac{5}{2} + 2 = \frac{9}{2}$.For a sequence to be an $AP$,the difference between any two consecutive terms must be constant. Although $a_{2} - a_{1} = a_{3} - a_{2} = -\frac{1}{2}$,the difference $a_{4} - a_{3} = \frac{9}{2}$.Since the common difference is not constant throughout the sequence,it does not form an $AP$.

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

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