How do you give a recursive formula for the arithmetic sequence where the 4th term is 3; 20th term is 35?

1 Answer

Answer:

Refer to explanation

Explanation:

The general formula for arithmetic progression is

#a_n=a_1+(n-1)*d# where

#a_n# is the n-th term in the sequence
#a_1# is the first term in the sequence
#d# is the common difference

We know that #a_4=3# and #a_20=35# so

#a_20-a_4=(a_1+19d)-(a_1+3d)=16d=> 16d=32=>d=2#

Hence the formula becomes
#a_n=a_1+2*(n-1)#

for #n=4# we have that

#a_4=a_1+6=>a_1=3-6=>a_1=-3#

Finally we have that #a_n=-3+2*(n-1)#