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