Tamil Nadu Board of Secondary EducationHSC Science Class 11th

Find the sum of the first 20-terms of the arithmetic progression having the sum of first 10 terms as 52 and the sum of the first 15 terms as 77 - Mathematics

Sum

Find the sum of the first 20-terms of the arithmetic progression having the sum of first 10 terms as 52 and the sum of the first 15 terms as 77

Solution

Sum of the first n terms of an Arithmetic progression is Sn =  [2a + (n – 1)d]

Given S10 = 52

52 = 10/2[ 2a + (10 – 1)d]

52 = 5[2a + 9d]

52 = 10a + 45d   ......(1)

Also given S15 = 77

77 = 152[2a + (15 – 1)d]

77 = 152[2a + 14d]

77 = 15[a + 7d]

77 = 15a + 105d   .......(2)

(1) × 15 ⇒ 780 = 150a +   675d
(2) × 10 ⇒ 770 = 150a + 1050d
10 =    0   –    375d

d = 10/(- 375)

= - 2/75

Substituting the value of d in (1)

52 = 10"a" + 45(- 2/75)

52 = 10"a" - 6/5

10a = 52 + 6/5

= (260 + 6)/5

= 266/5

a = 266/(5 xx 10)

= 133/25

S20 = 20/2[2 xx 133/25 + 19 xx (-2)/75]

= 10[266/25 - 18/75]

= 10[(798- 38)/75]

= 10[760/75]

S20 = 2 xx 760/15

= 2 xx 152/3

= 304/3

Concept: Finite Series
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APPEARS IN

Tamil Nadu Board Samacheer Kalvi Class 11th Mathematics Volume 1 and 2 Answers Guide
Chapter 5 Binomial Theorem, Sequences and Series
Exercise 5.3 | Q 1 | Page 220
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