The given sequence is a geometric sequence, where the common ratio (r) between any two consecutive terms is:
r = 3/1.5 = 2
We need to find the sum of the first 10 terms of this sequence. Let's denote the first term (a₁) as 1.5 and the tenth term (a₁₀) as a.
The formula to find the sum of the first n terms of a geometric sequence is:
Sₙ = a(1 - rⁿ)/(1 - r)
Substituting the values, we get:
a = 1.5 x 2^9 = 768
S₁₀ = 1.5(1 - 2¹⁰)/(1 - 2) = 1.5(1 - 1024)/(-1) = 1.5 x 1023
Therefore, the sum of the first 10 terms of the given sequence is 1.5 x 1023, which is approximately equal to 1.53 x 10³=1534,5