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2c, 3c, 12, and 19 pls explain :(. this is arithmetic and geometric series/sequences questionsB91D1889-8336-4B53-A561-03B5D979975F.jpeg9037C503-4DA8-4ECB-BFA1-3155405C84BB.jpeg50BC89D5-DD54-4BB0-9F09-64FC1C775DA3.jpeg

50BC89D5-DD54-4BB0-9F09-64FC1C775DA3.jpeg
19.
Write the number 3.2141414... as a series of fractions and find the sum to determine the
equivalent fraction form of the number. [3 marks]
9037C503-4DA8-4ECB-BFA1-3155405C84BB.jpeg
r= 3
+, ( 3) 5 = 1458 = 6
56 = 3 ( 1458 ) - 6
12.
How many terms are in the geometric sequence where the first'term is 512x", the common ratio
( 3-1)
is - and the last term is x31? [3 marks]
+, = 512 x4
r= x
* 31 = ( 512 x 4) x 3 , nd
2
n = x 31
B91D1889-8336-4B53-A561-03B5D979975F.jpeg
2.
Find the common difference and the first term of each arithmetic sequence with the given
conditions. [6 marks]
a.
The 8th term is 33 and the 14" term is 57.
33+ 6d = 57
+ + 7 ( 4 ) =33
6d = 24
728 71
d = 4
b.
The 5th term is -20 and the 18th term is -59.
t,=-8 d= -3
-20+ 13d = -59
Xo c.
The 7th term is 3 + 5x and 11" term is 3 + 23x.
13d =- 39
d =- 3
-39
3.
Write the general term (simplified) for each sequence in question 2. [3 marks]
a. a) + = +, + (n-1)d, b) th = t, + ( n-1)d
b.
th = 5 4 (n-1) ( 4)
th = - 8 + ( n- 1) - 3
to = 4n + 1
tn = 30- 5
C.

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