Algebra form of the sequence 10,17,24
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The arithmetic sequence 10, 17, 24.
Here, First term a=10
The common difference d=17-10=7
The nth term of the sequence is
an= a+(n-1)d
an=10+(n-1)7
an=10+7n-7
an=7n+3
Let x be a natural number and its square is the nth term,
x²=7n+3
x²-3=7n
n=x²-3/7
Now, for all integers from 0 to 30, n does not come out to be an integer.
Therefore, the arithmetic sequence 10, 17, 24… contains no perfect squares.
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