# Q: 4    Which of the following are APs ? If they form an AP, find the common difference d and write three more terms.                 (xv)  $\small 1^2,5^2,7^2,73,...$

G Gautam harsolia

Given series is
$\small 1^2,5^2,7^2,73,...$
we can rewrite it as
$1,25,49,73....$
Now,
first term to this series is = 1
Now,
$a_1 =1 \ \ and \ \ a_2 = 25 \ \ and \ \ a_3 =49 \ \ and \ \ a_4 = 73$
$a_2-a_1 = 25-1 = 24$
$a_3-a_2 = 49-25=24$
$a_4-a_3 = 73-49=24$
We can clearly see that difference between terms are  equal and equal to 24
Hence, given series is  in AP
Now, next three terms are
$a_5=a_4+d = 73+24=97$
$a_6=a_5+d = 97+24=121$
$a_7=a_6+d = 121+24=145$
Therefore, next three terms of given series are 97,121,145

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