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