a) Determine the common ratio and the sixth term of the following geometric sequence.4, -12,36....... b) Determine the sum of the first eight terms of the series

a) Determine the common ratio and the sixth term of the following geometric sequence.4, -12,36.......
b) Determine the sum of the first eight terms of the series
c) The twelve term of an A.P is five times the second term and the sum of the first ten terms of the series is 120. Find the value of the first term and the common difference

Answers

a) 4,12,36, ...............

Common ratio

r = -$\frac{12}{4}$ = -3

n^th term of a G.P = ar^n-1

6^th term = ar^6-1

= 4(-3)⁵ = 4(-243)

= -972

b) S_n = a$\frac{1-r^n}{1-r}$

S_{8 = 4$\frac{(1-(-3)^8)}{1-(-3)}$

S₈ = -6 560

c) 12^th} term

= 5 times (second term)

a + 11d = 5(a+d)

a + 11d = 5a + 5d

6d = 4a therefor a = $\frac{6d}{4}$

120 = $\frac{10}{2}(2a+9d)$

240 = 20a + 90d

240 = $\frac{120d}{4}$ + 90d

240 = 30d + 90d

240 = 120d d = 2

But a = $\frac{6d}{4}$

a = $\frac{6\times 2}{4}\; = \frac{12}{4}\; = 3$

the first term is 3 and the common difference is 2

johnmulu answered the question on March 8, 2017 at 14:01

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