Question 4 (xii)
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(xii) √2,√8,√18,√32……
(xii) √2,√8,√18,√32……
Here,
a2−a1=√8−√2=2√2−√2=√2a3−a2=√18−√8=3√2−2√2=√2a4−a3=√32−√18=4√2−3√2=√2
⇒an+1−an is same everytime.
Therefore,d=√2 and the given numbers are in A.P.
Next three terms are:
a5=√32+√2=4√2+√2=5√2=√50a6=5√2+√2=6√2=√72a7=6√2+√2=7√2=√98