Question 4 (xv)
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(xv) $1^{2}, 5^{2}, 7^{2}, 7^{3} \dots \dots$

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Solution

(xv)
$1^{2}, 5^{2}, 7^{2}, 73 \dots \dots O r, 1, 25, 49, 73 H e r e, a_{2} - a_{1} = 25 - 1 = 24 a_{3} - a_{2} = 49 - 25 = 24 a_{4} - a_{3} = 73 - 49 = 24 \Rightarrow a_{n + 1} - a_{n} i s s a m e e v e r y t i m e T h e r e f o r e, d = 24 a n d t h e g i v e n n u m b e r s a r e i n A . P . N e x t t h r e e t e r m s a r e : a_{5} = 73 + 24 = 97 a_{6} = 97 + 24 = 121 a_{7} = 121 + 24 = 145$

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Question 4 (xv) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (xv) 12,52,72,73……

(xv) 12,52,72,73……Or, 1,25,49,73Here,a2−a1=25−1=24a3−a2=49−25=24a4−a3=73−49=24⇒an+1−an is same everytimeTherefore, d=24 and the given numbers are in A.P.Next three terms are:a5=73+24=97a6=97+24=121a7=121+24=145

Question 4 (xv)
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(xv) $1^{2}, 5^{2}, 7^{2}, 7^{3} \dots \dots$