Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10th
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The sum of first n terms of a certain series is given as 2n2 – 3n. Show that the series is an A.P. - Mathematics

Sum

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

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Solution

Given Sn = 2n2 – 3n

S1 = 2(1)2 – 3(1) = 2 – 3 = – 1

⇒ t1 = a = – 1

S2 = 2(22) – 3(2) = 8 – 6 = 2

t2 = S2 – S1 = 2 – (– 1) = 3

∴ d = t2 – t1 = 3 – (– 1) = 4

Consider a, a + d, a + 2d, ….….

– 1, – 1 + 4, – 1 + 2(4), …..…

– 1, 3, 7, ….

Clearly, this is an A.P. with a = – 1, and d = 4.

Concept: Series
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APPEARS IN

Samacheer Kalvi Mathematics Class 10 SSLC Tamil Nadu State Board
Chapter 2 Numbers and Sequences
Exercise 2.6 | Q 4 | Page 67
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