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The sum of first n terms of an A.P is 5n2 + 3n. If its mth terms is 168, find the value of m. Also, find the 20th term of this A.P. - Mathematics

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Question

The sum of first n terms of an A.P is 5n2 + 3n. If its mth terms is 168, find the value of m. Also, find the 20th term of this A.P.

Sum
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Solution

Sn = 5n2 + 3n

Put n = 1

S1 = T1 = 5 + 3 = 8

Put n = 2

S2 = 5(2)2 + 3 + 2 = 26

T2 = S2 – S1 = 26 – 8 = 18

S3 = 5(3)2 + 3 + 3 = 54

T3 = S3 – S2 = 54 – 26

= 28

Therefore, first term, a = 8 and common difference = 18 – 8 = 10 

Tm = a + (m – 1) d 

168 = 8 + (m – 1) 10

168 = 8 + 10m – 10

170 = 10m

m = 17

T20 = 8 + (20 – 1) 10

= 8 + 19 × 10

= 198

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Chapter 5: Arithmetic Progression - Exercise 5.6 [Page 53]

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RD Sharma Mathematics [English] Class 10
Chapter 5 Arithmetic Progression
Exercise 5.6 | Q 42 | Page 53

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