Question

Can someone help please

Answer 1

3a. (i). Sequence
`V_(n)` is in Arithematic

(ii). Sequence
`W_(n)` is in Geometric

3b. 2520 Sum of First 20 Arithmetic Sequence

3c. 98292 Sum of First 13 Geometric Sequence

Explanation:

According to the Question,

3a. (i) Arithmetic Sequence (
`V_(n)`) = 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 (
`W_(n)`) = 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,
`S_(n)=(n)/(2)[2a + (n-1) d]`

(Where, a=first term of sequence , n= number of term & d=common difference)

`S_(n)`=10[2×12 + 19×12]

`S_(n)` =10×252 ⇔ 2520

3c. Sum Of First 13 term of a geometric sequence,
`S_(n)= (a(r^(n)-1) )/(r-1)`

(Where, a=first term of sequence , n= number of term & r= common ratio)

`S_(n)`=12(
`2^(13)`-1) / 2-1

`S_(n)`=12×8191 ⇔ 98292