Consider the infinite geometric sequence 25 , 5 , 1 , 0.2 , ... (a) Find the common ratio. (b) Find (i) the 10th term; (ii) an expression for the nth term. (c) Find the sum of the infinite sequence.
QUESTION (a) R = U(n+1)/U(n ) = 5/25= 0.2(b) (i) U(10) = 25 x (1/5)^9 = 0.0000128 (ii) U(n) = 25 x (1/5)^(n-1)(c) S = U(1)/(1-r) = 25/(1-(1/5))=25/(4/5))=125/4=31.25
CR
Related Maths IB answers
All answers ▸How do you calculate the probability P(X < x) for a normally distributed random variable X?
A sequence of numbers have the property that x, 12, y, where x > 0, y > 0, form a geometric sequence while 12, x, 3y form an arithmetic sequence. A)If xy = k, find k. B)Find the value of x and y.
Consider the arithmetic sequence 2, 5, 8, 11, ... a) Find U101 b) Find the value of n so that Un = 152
Find the cube roots of i in the form a+bi, where a, b are real numbers.