Question
Is the given sequence:$1^2, 5^2, 7^2, 73, .....$ forms an AP? If it forms an AP, then find the common difference d and write the next three terms.
✓
Answer
We have given the numbers as follows: $1^2, 5^2, 7^2, 73.....$
now find
$a_2 - a_1 = 5^2 - 1 = 25 - 1 = 24$
$a_3 - a_2 = 7^2 - 5^2 = 49 - 25 = 24$
$a_4 - a_3 = 73 - 7^2 = 73 - 49 = 24$
As, the common difference is the same. The sequence is in A.P.
Next three terms are: $a_5= a_4+ d = 73 + 24 = 97$
$a_6= a_5+ d = 97 + 24 = 121$
$a_7= a_6+ d = 121 + 24 = 145$
now find
$a_2 - a_1 = 5^2 - 1 = 25 - 1 = 24$
$a_3 - a_2 = 7^2 - 5^2 = 49 - 25 = 24$
$a_4 - a_3 = 73 - 7^2 = 73 - 49 = 24$
As, the common difference is the same. The sequence is in A.P.
Next three terms are: $a_5= a_4+ d = 73 + 24 = 97$
$a_6= a_5+ d = 97 + 24 = 121$
$a_7= a_6+ d = 121 + 24 = 145$
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