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Mathematics

The 7th term of the given Arithmetic Progression (A.P.):

1a,(1a+1),(1a+2),......\dfrac{1}{a}, \Big(\dfrac{1}{a} + 1\Big), \Big(\dfrac{1}{a} + 2\Big), …… is :

  1. (1a+6)\Big(\dfrac{1}{a} + 6\Big)

  2. (1a+7)\Big(\dfrac{1}{a} + 7\Big)

  3. (1a+8)\Big(\dfrac{1}{a} + 8\Big)

  4. (1a+77)\Big(\dfrac{1}{a} + 7^7\Big)

AP GP

ICSE 2024

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Answer

In the A.P. :

1a,(1a+1),(1a+2),......\dfrac{1}{a}, \Big(\dfrac{1}{a} + 1\Big), \Big(\dfrac{1}{a} + 2\Big), ……

First term (x) = 1a\dfrac{1}{a}

Common difference (d) = 1a+11a\dfrac{1}{a} + 1 - \dfrac{1}{a} = 1.

x7 = x + (7 - 1)d

= 1a+6×1\dfrac{1}{a} + 6 \times 1

= (1a+6)\Big(\dfrac{1}{a} + 6\Big).

Hence, Option 1 is the correct option.

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