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Arithmetic Progressions — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsArithmetic Progressions3 Marks
Question
Which of the following sequences are arithmetic progressions. For those which are arithmetic progressions, find out the common difference.
$\frac{1}{2},\frac{1}{4},\frac{1}{6},\frac{1}{8}, .....$
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Answer

In the given problem, we are given various sequences.
We need to find out that the given sequences are an A.P. of not and then find its common difference (d).
$\frac{1}{2},\frac{1}{4},\frac{1}{6},\frac{1}{8}, .....$
in the given sequance
$\text{a}_1=\frac{1}{2},\text{a}_2=\frac{1}{4},\text{a}_3=\frac{1}{6},\text{a}_4=\frac{1}{8}.$
Check the condition
$a_2 - a_1 = a_3 - a_2$
$\frac{1}{4}-\frac{1}{2}=\frac{1}{6}-\frac{1}{4}$
$\frac{1-2}{4}=\frac{4-6}{24}$
$\frac{-1}{4}=-\frac{2}{24}$
$\frac{-1}{4}\neq\frac{-1}{12}$
Condition is not sarisfied
$\therefore$ Given sequnce not in A.P.

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