Tamil Nadu Board of Secondary EducationHSC Arts Class 11th

# Find the value of n, if the sum to n terms of the series 3+75+243+...... is 4353 - Mathematics

Sum

Find the value of n, if the sum to n terms of the series sqrt(3) + sqrt(75) + sqrt(243) + ...... is 435 sqrt(3)

#### Solution

t1 = sqrt(3)

t2 = sqrt(75)

= sqrt(25 xx 3)

= 5sqrt(3)

t3 = sqrt(243)

= sqrt(81 xx 3)

= 9sqrt(3)

Here t1 = sqrt(3)

t2 = 5sqrt(3)

t3 = 9sqrt(3)

(i.e) a = sqrt(3)

d = 5sqrt(3) - sqrt(3)

= 4sqrt(3)

Sn = "n"/2[2"a" + ("n" - 1)"d"]

= 435 sqrt(3)  ......(Given)

⇒ "n"/2 [2sqrt(3) + ("n" - 1)4sqrt(3)] = 435sqrt(3)

⇒ ("n" sqrt(3))/2 [2 + 4"n" - 4] = 435 sqrt(3)

⇒ n[4n – 2] = 870

4n2 – 2n – 870 = 0

(÷ by 2)2n2 – n – 435 = 0

2n2 – 30n + 29n – 435 = 0

⇒ 2n(n – 15) + 29(n – 15) = 0

(2n + 29)(n – 15) = 0

⇒ n = (-29)/2 or 15

n = (-29)/2 not possible,

So n = 15

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 6 | Page 220
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