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Mathematics

The next two terms of the arithmetic progression (A.P.) 5,20,45,......\sqrt{5}, \sqrt{20}, \sqrt{45}, …… are :

  1. 9 and 959\sqrt{5}

  2. 45 and 554\sqrt{5} \text{ and } 5\sqrt{5}

  3. 25 and 552\sqrt{5} \text{ and } 5\sqrt{5}

  4. 2 and 353\sqrt{5}

AP GP

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Answer

Given,

A.P. = 5,20,45,......\sqrt{5}, \sqrt{20}, \sqrt{45}, ……

= 5,25,35,......\sqrt{5}, 2\sqrt{5}, 3\sqrt{5}, ……

So, above A.P. has first term (a) = 5\sqrt{5}

Common difference (d) = 25−5=52\sqrt{5} - \sqrt{5} = \sqrt{5}

Next terms of A.P. are 4th and 5th.

Given,

an = a + (n - 1)d

So,

a4 = a + (4 - 1)d

= 5+3×5\sqrt{5} + 3 \times \sqrt{5}

= 5+35\sqrt{5} + 3\sqrt{5}

= 454\sqrt{5}.

a5 = a + (5 - 1)d

= 5+4×5\sqrt{5} + 4 \times \sqrt{5}

= 5+45\sqrt{5} + 4\sqrt{5}

= 555\sqrt{5}.

Hence, Option 2 is the correct option.

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