Find the common difference for the arithmetic progression
$3 + 2 \sqrt{2}, 3 + 4 \sqrt{2}, 3 + 6 \sqrt{2}, 3 + 8 \sqrt{2}$

3 + \sqrt{2}

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3

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\sqrt{2}

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2 \sqrt{2}

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Solution

The correct option is D $2 \sqrt{2}$
Common difference is the difference between two consecutive terms in an arithmetic sequence.
$∴$ Common difference is:
$(3 + 4 \sqrt{2}) - (3 + 2 \sqrt{2}) = 2 \sqrt{2}$
(or)
$(3 + 6 \sqrt{2}) - (3 + 4 \sqrt{2}) = 2 \sqrt{2}$
(or)
$(3 + 8 \sqrt{2}) - (3 + 6 \sqrt{2}) = 2 \sqrt{2}$

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Similar questions

Q. The common difference for the arithmetic progression

3 + 2 \sqrt{2}, 3 + 4 \sqrt{2}, 3 + 6 \sqrt{2}, 3 + 8 \sqrt{2}

Find the common difference of the following arithmetic progression.
$3 + 2 \sqrt{2}, 3 + 4 \sqrt{2}, 3 + 6 \sqrt{2}, 3 + 8 \sqrt{2}$

Find the common difference and write the next four terms of each of the following arithmetic progressions:
(i) $1, - 2, - 5, - 8, \dots$
(ii) $0, - 3, - 6, - 9, \dots$
(iii) $- 1, \frac{1}{4}, \frac{3}{2}, \dots$
(iv) $- 1, - \frac{5}{6}, - \frac{2}{3}, \dots$

Q. Find out which of the following sequences are arithmetic progressions. For those which are arithmetic progressions, find out the common difference.

1^{2}, 3^{2}, 5^{2}, 7^{2}, . . .

Q. Find the common difference and write the next four terms of each of the following arithmetic progression:

- 1, - \frac{5}{6}, - \frac{2}{3}, . . .

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Find the common difference for the arithmetic progression 3+2√2, 3+4√2, 3+6√2, 3+8√2

The correct option is D 2√2Common difference is the difference between two consecutive terms in an arithmetic sequence. ∴ Common difference is: (3+4√2)−(3+2√2)=2√2 (or) (3+6√2)−(3+4√2)=2√2 (or) (3+8√2)−(3+6√2)=2√2

Find the common difference for the arithmetic progression
$3 + 2 \sqrt{2}, 3 + 4 \sqrt{2}, 3 + 6 \sqrt{2}, 3 + 8 \sqrt{2}$