Question
Is the given sequence: $1^2, 3^2, 5^2, 7^2, ......$ forms an $AP?$ If it forms an $AP,$ then find the common difference $d$ and write the next three terms.
✓
Answer
The given terms can be written as follows:
$1, 9, 25, 49,....$
$ \text { Here, } a_2-a_1=9-1=8$
$ a_3-a_2=25-9=16$
$a_4-a_3=49-25=24$
$\text { Since } a_{k+1}-a_k \text { is not same for all values of } k$
Hence, it is not an $AP$. So we can not find next three terms.
$1, 9, 25, 49,....$
$ \text { Here, } a_2-a_1=9-1=8$
$ a_3-a_2=25-9=16$
$a_4-a_3=49-25=24$
$\text { Since } a_{k+1}-a_k \text { is not same for all values of } k$
Hence, it is not an $AP$. So we can not find next three terms.
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