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Arithmetic Progressions — Maths STD 10 — Question

Gujarat 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.
$1^2, 5^2, 7^2, 73, .....$
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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 $(d),$
Here,
First term $(a)=1^2$
$ a_1=5^2 $
$ a_2=7^2$
Now, for the given to sequence to be an $A.P.$
Common difference $(\mathrm{d})=\mathrm{a}_1-\mathrm{a}=\mathrm{a}_2-\mathrm{a}_1$
Here,
$ a_2-a_1=5^2-1^2 $
$ =25-1$
$ =24$
Also,
$a_3-a_2=7^2-5^2=49-25=24$
Since $a_1- a = a_2 - a_1$
Hence, the given sequence is an $A.P.$ with the common difference $d = 24.$

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