# Find the value of x so that x+2,5x+1,x+11 will form a geometric sequence.justify your answer.find the sum of the first 10 terms of the given sequence

1
by jhunajean1

• Brainly User
2016-07-21T11:58:35+08:00
x = 1
Sum of the first ten terms = 3,069

-----------------------------------------------------

Solution:

5x + 1           x + 11
-----------  =   -----------
x + 2             5x + 1

(5x + 1) (5x + 1) = (x + 2) (x + 11)

25x² + 10x + 1 = x² + 13x + 22

25x² - x² + 10x - 13x + 1 - 22 = 0

24x² - 3x - 21 = 0

Solve by factoring:

(3x - 3) (8x + 7) = 0

3x - 3 = 0                 8x + 7 = 0
3x = 3                      8x = -7
3x/3 = 3/3                8x/8 = -7/8

x = 1                        x = -7/8

If x =1:
x + 2     ⇒ 1 + 2 = 3
5x + 1   ⇒ 5(1) + 1 = 6
x + 11   ⇒ 1 + 11 = 12

The geometric sequence is 3, 6, 12, ..., a₁₀

Common ratio is 2.
6/2 = 2
12/6 = 2

Sum of the first 10 terms of the sequence:
a₁ = 3      r = 2         n = 10         S₁₀=?

a₁ (1 - r¹⁰)
S₁₀ =  ----------------
1 - r

3 [ 1 - (2)¹⁰]
S₁₀ = --------------------
1 - 2

3 [ 1 - 1024 ]
S₁₀ =  --------------------
-1

3 (-1023)
S₁₀ =  -------------------
-1

-3069
S₁₀ =  -----------
-1

S₁₀ = 3,069  ⇒    Sum of the first ten terms