Question

Check whether
3,
$3 + \sqrt{2}$
,
$3 + 2 \sqrt{2}$
,
$3 + 3 \sqrt{2}$
are in arithmetic progression.
​

Answer 1

Answer:

Not are in arithmetic progression.

Step-by-step explanation:

Because different between two terms are not constant.

I solve it.

There are formula to solve

that is

d = t2 - t1

d =t3 - t2

d = t4 -t3

d is not constant.

Therefore it is not A.P.

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Answer 2

$\large\boxed{\fcolorbox{blue}{yellow} {Answer}}$

The given sequence is an Arithmetic Progression.

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The given sequence is

3, 3 + √2, 3 + 2√2, 3 + 3 √2

Now, here

t1 = 3,

t2 = 3 + √2,

t3 = 3 + 2 √2,

t4 = 3 + 3 √2

Now,

t2 - t1 = 3 + √2 - 3 = √2

t3 - t2 = (3 + 2√2) - (3 + √2) = 3 + 2√2 - 3 - √2 = √2

t4 - t3 = (3 + 3√2) - (3 + 2√2) = 3 + 3√2 - 3 - 2√2 = √2

Here, common difference d which is √2 is constant between two consecutive terms in the given sequence.

∴ The given sequence is an Arithmetic Progression.

Hope it helps!

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