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USE CODE: omar10

Find Sum of First nth Term of AP 

Illustration:

Let sum of n terms of a series be n (2n–1). Find its mth terms.

 Solution:

 Let Sm and Sm–1 denote the sum of first m and (m – 1) terms respectively.

Sm = T1 + T2 + T3 + ……. + Tm–1 + Tm

Sm = T1 + T2 + T3 + ……. + Tm–1

Subtracting

Sm – Sm–1 = Tm

⇒ Tm = (m(2m–1))–(m–1)(2(m–1)–1))

        = (2m2 – m)–(2m2 – 5m + 3)

        = 4m – 3

 

Illustration:

        The sum of n terms of two A.P.’s are in the ratio 3n + 2: 2n+3. Find  the ratio of their 10th terms.

Solution:

        Let a, a + d, a + 2d, a + 3d, ……………

        A, A + D, A + 2D, A + 3D, ………………

        be two A.P.’s

            n/2[2a+(n–1)d]/n/2[2A+(n–1)d] = 3n+2/2n+3       (given)

        ⇒ a+n–1/2d/A+n–1/2D = 3n+2/2n+3

        ⇒ To get the ratio of 10th terms put n–1/2 = 9

                       or n = 19

        ⇒ a+9d/A+9D = 3(19)+2/2(19)+3 = 59/41

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USE CODE: omar10