Answer:
3a. (i). Sequence [tex]V_{n}[/tex] is in Arithematic
(ii). Sequence [tex]W_{n}[/tex] is in Geometric
3b. 2520 Sum of First 20 Arithmetic Sequence
3c. 98292 Sum of First 13 Geometric Sequence
Step-by-step explanation:
According to the Question,
3a. (i) Arithmetic Sequence ([tex]V_{n}[/tex]) = 12 , 24 , 36 , 48 .....
it is a sequence of numbers such that the difference between the consecutive terms is same. example → 24+12=12 , 36-24=12 , 48-36=12 ∵Common Difference=12
(ii) Geometric Sequence ([tex]W_{n}[/tex]) = 12 , 24 , 48 , 96 .....
A geometric series is a series for which the ratio of each two consecutive terms is a constant function. example → 24/12= 2 , 48/24= 2 , 96/48= 2 ∵Common Ratio=2
3b. Sum of first 20 terms of Arithematic sequence, [tex]S_{n}=\frac{n}{2}[2a + (n-1) d][/tex]
(Where, a=first term of sequence , n= number of term & d=common difference)
[tex]S_{n}[/tex]=10[2×12 + 19×12]
[tex]S_{n}[/tex] =10×252 ⇔ 2520
3c. Sum Of First 13 term of a geometric sequence, [tex]S_{n}= \frac{a(r^{n}-1) }{r-1}[/tex]
(Where, a=first term of sequence , n= number of term & r= common ratio)
[tex]S_{n}[/tex]=12([tex]2^{13}[/tex]-1) / 2-1
[tex]S_{n}[/tex]=12×8191 ⇔ 98292