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Question

Which of the following series forms an AP?

(i) a – 2d, a – d, a, a + d, a + 2d                                                   

(ii)a, a + d, a + 2d, a + 3d, a + 4d

(iii) a – 3d, a – d, , a + d, a + 3d    


  1. Only (ii) and (iii)

  2. All (i),(ii) and (iii)

  3. Only (i) and (iii)

  4. Only (i) and (ii)  


Solution

The correct option is B

All (i),(ii) and (iii)


Consider each series(i) a – 2d, a – d, a, a + d, a + 2d

Difference between first two consecutive terms = a – d –(a – 2d) = d

Difference between third and second consecutive terms = a – (a – d) = d

Difference between fourth and third consecutive terms = a + 2d – (a + d) = d

Since a2 – a1 = a3 – a2= a4 – a3

This series is an AP

Consider each series(ii) a, a + d, a + 2d, a + 3d, a + 4d      

Difference between first two consecutive terms = a + d –a = d

Difference between third and second consecutive terms = a + 2d - (a + d) = d

Difference between fourth and third consecutive terms = a + 3d – (a +2d) = d

Since a2 – a1 = a3 – a2 = a4 – a3

This series is an AP

(iii) a – 3d, a – d, a + d, a + 3d

Difference between first two consecutive terms = a – d – (a – 3d) = 2d

Difference between third and second consecutive terms = a + d – (a – d) = 2d

Difference between fourth and third consecutive terms = a +3d – (a +d) = 2d

Since a2 – a1 = a3 – a2 = a4 – a3

This series is an AP

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