1. A sequence starts with the number 48 and has a common difference of ‒13.
(1) Write a function that describes this sequence.
(2) Find the 20th term of this sequence.
Answers
Step-by-step explanation:
Given :-
A sequence starts with the number 48 and has a common difference of ‒13.
To find :-
(1) Write a function that describes this sequence.
(2) Find the 20th term of this sequence.
Solution :-
Given that
The starting number of the sequence = 48
First term =(a) = 48
Common difference =(d) = -13
The sequence is the Arithmetic Progression
We know that
The general term of the AP
=> an = a+(n-1)d
On Substituting these values in the above formula
=> an = 48+(n-1)(-13)
=> an = 48-13n +13
=> an = 61-13n
The function describes the given sequence is 61-13n
20th term of the sequence = a 20
=> a 20 = a+(20-1)d
=> a 20 = a +19d
=> a 20 = 48 + 19(-13)
=> a 20 = 48 +(-247)
=> a 20 = 48-247
=> a 20 = -199
(or)
General term = an = 61-13n
If n= 20 then a 20
=> 61- (13)(20)
=> 61 - 260
=> -199
Therefore, a 20 = -199
Answer:-
1)The function describes the given sequence is 61-13n
2) The 20th term of the given sequence is -199
Used formulae:-
The general term of the AP= an = a+(n-1)d