Q17 of 110 Page 53

Show that the sum of an arithmetic series whose first term is a, second term b and the last is c is equal to


First term = a

Common difference = (b–a)


Last term = c


⇒ c = a + (n–1)(b–a)


⇒ (n–1) = (c–a) / (b–a)


⇒ n = (b + c – 2a) /( b – a)


Sum of terms =


⇒ Sum of terms =


Hence proved.


More from this chapter

All 110 →
15

The sum of first n terms of a certain series is given as 3n2– 2n. Show that the series is an arithmetic series.

 16

If a clock strikes once at 1 o’clock, twice at 2 o’clock and so on, how many times will it strike in a day?

 18

If there are (2n + 1) terms in an arithmetic series, then prove that the ratio of the sum of odd terms to the sum of even terms is (n + 1) : n.

 19

The ratio of the sums of first m and first n terms of an arithmetic series is m2: n2show that the ratio of the mth and nth terms is (2m – 1) : (2n – 1)