Which of the following are explicit equations for the nth term of some kind of arithmetic sequence? a) pn=p1+(n-1)p1 b) an=an-1+d c) xn=x1(n-1) d) xn=xn-1+vt e) pn=pn-1+ip1

The required equation is

Step-by-step explanation:

To find : Which of the following are explicit equations for the nth term of some kind of arithmetic sequence?    

Solution :

The Explicit formula which shows the nth term of a sequence in terms of n is given by,

Where, is the nth term

is the first term

n is the number of terms

d is the common difference

Therefore, The required equation is

the answer is c

hope this !

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for