for an arithmetic sequence is 1a= 21. is the recursive formula is an=an-1+1. which expensive formula can be used to find the nth term in the sequence

Answer 1

Recursive formula is

a_n = a_n-1 + d

where d = common difference

Explicit formula is

a_n = a_1 + d*(n-1)

It kind of resembles point slope formula if you are looking at the first point (1, a1) which is (1,21)

(y - y1= m(x-x1) for comparison —> y = y1 + m(x-x1))

a_n is like y, stays a variable

a_1 is like y1 = 21

x1 will be = 1

d is like the slope = + 1

n is like x, stays a variable

explicit formula

a_n = 21 + 1(n-1)

Answer 2

the nth term is one more than the previous term

an = an-1 +1

a1 = 21

a2 = 22

a3 = 23

an = an-1 +1

a21 = a20 + 1

a21 = a19+2

a21 = a18+3

a21 = a17+4

a21 = a1+20

a21 =21+20 = 41

a21 =41

the 21st term = 41 = 21 + 20= a1 + n-1

the 2nd term = 21+1 = 22= a1 + n-1

the nth term = a1+n-1 = 21+n-1 = n+20

an = n+20