Question

Can this question can be explain here please in vedio
3,3+root2,3+2root2,3+3root2

Answer 1

Answer:

This an (AP) Arithmetic Progession sum .

We have to prove the given sequence is in AP or not . So we have to find the common difference(d).

If the d is constant then we can say this sequence is in AP .

We need to find three conditions to prove the (d) as constant .

Step-by-step explanation:

The given sequence is

3 , 3+√2 , 3+2√2 , 3+3√2

First term = a = t1 = 3

= t2 = 3+√2

= t3 =3+2√2

= t4 =3+3√2

1. Common difference (d) = t2 - t1

= 3+√2- (3)

= 3+√2-3

=√2 ___________ (1)

2. d = t3 - t2

= 3+2√2 - (3+√2)

= 3 +2√2 - 3- √2

= 3 - 3 + 2√2 - √2

= √2 ___________________ (2)

3. d = t4 - t3

= 3+3√2-(3+2√2)

= 3 + 3√2- 3- 2√2

= 3- 3 + 3√2- 2√2

= √2 _____________________(3)

Therefore, the common difference is √2 .

The common difference is constant ____[From (1),(2)&(3)]

Thus the Given sequence i.e

3, 3+√2, 3+2√2, 3+3√2 is in A.P.

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