In the page geometric sequence worksheet solution3 you are going to see solution of each questions from the geometric series worksheet.

(6) If the geometric sequences 162,54,18,......... and 2/81,2/27,2/9,.......... have their nth term equal,find the value of n.

**Solution:**

Since nth term of the given geometric sequence are equal let us find nth term of the given sequences one by one.

162,54,18,.........

a = 162 r = 54/162

r = 1/3

2/81,2/27,2/9,..........

a = 2/81 r = (2/27)/ (2/81)

= 2/27 x 81/2

r = 3

t n = a r^(n-1)

= 162 (1/3)^(n-1)

= 162 (3⁻¹)^(n-1)

= 162 (3⁻ⁿ⁺¹) ------ (1)

t n = a r^(n-1)

= (2/81) x (3)^(n-1) ------ (2)

t n = t n

162 (3⁻ⁿ⁺¹) = (2/81) x (3)^(n-1)

[(162 x 81)/2] (3⁻ⁿ⁺¹) = (3)^(n-1)

(81 x 81)(3⁻ⁿ⁺¹) = (3)^(n-1)

(3⁴ x 3⁴)(3⁻ⁿ⁺¹) = (3)^(n-1)

(3⁸)(3⁻ⁿ⁺¹) = (3)^(n-1)

(3)⁻ⁿ ⁺ ⁹ = (3)^(n-1)

- n + 9 = n - 1

- n - n = -1 - 9

-2 n = -10

n = 10/2

n = 5

from this we can decide 5th term of those sequence are equal.

(7) The fifth term of a G.P is 1875.If the first term is 3,find the common ratio.

**Solution:**

Fifth term = 1875

First term = 3

t₅ = 1875

a = 3

a r⁴ = 1875

3 r⁴ = 1875

r⁴ = 1875/3

r⁴ = 625

r⁴ = 5⁴

r = 5

Therefore the common ratio is 5.

(8) The sum of three terms of a geometric sequence is 39/10 and their product is 1. Find the common ratio and the terms.

**Solution:**

Let the first three terms are a/r,a,ar

Sum of three terms = 39/10

Product of three terms = 1

(a/r) + a + a r = 39/10 ------ (1)

(a/r) x a x a r = 1

a³ = 1³

a = 1

Substitute a = 1 in the first equation

(1/r) + 1 + 1 r = 39/10

(1 + r + r²)/r = 39/10

10(1 + r + r²) = 39 r

10 r² + 10 r - 39 r + 10 = 0

10 r² - 29 r + 10 = 0

(2r - 5) (5r - 2) = 0

2 r - 5 = 0 5r - 2 = 0

2 r = 5 5 r = 2

r = 5/2 r = 2/5

a/r = 1/(5/2) a/r = 1/(2/5)

= 2/5 = 5/2

a = 1 a = 1

ar = 1(5/2) ar = 1(2/5)

= 5/2 = 2/5

Therefore the three terms are (2/5),1,(5/2) or (5/2),1,(2/5)

- Geometric sequence worksheet
- Geometric series worksheet
- Special series
- Sequence
- Arithmetic progression
- Arithmetic series
- Geometric progression
- Geometric series

you can get solution for remaining question in the next page.geometric sequence worksheet solution3 geometric sequence worksheet solution3