The best way for solving the question of arithmetic progressions of exercise 5.1 of class 10th math. Please suggest me the best way to solve this problem 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
Here,
a2 – a1 = 3+√2-3 = √2
a3 – a2 = (3+2√2)-(3+√2) = √2
a4 – a3 = (3+3√2) – (3+2√2) = √2
Since, an+1 – an or the common difference is same every time.
Therefore, d = √2 and the given series forms a A.P.
Hence, next three terms are;
a5 = (3+√2) +√2 = 3+4√2
a6 = (3+4√2)+√2 = 3+5√2
a7 = (3+5√2)+√2 = 3+6√2