An arithmetic sequence is represented by the recursive formula a1=17an=an−1−8 . What is the fourth term in the sequence? a4=−4 a4=−7 a4=−9 a4=−14

a₄ = - 15

Step-by-step explanation:

Using the recursive formula and a₁ = 17 , then

a₂ = a₁ - 8 = 17 - 8 = 9

a₃ = a₂ - 8 = 9 - 8 = 1

a₃ = a₂ - 8 = 1 - 8 = - 7

a₄ = a₃ - 8 = - 7 - 8 = - 15

with Step-by-step explanation:

We are given that

P(n)=

We have to prove that given statement is a multiple of 7 using mathematical induction for all natural numbers n belongs to N.

Suppose n=1

Then P(1)=8-1=7

Hence, it is a multiple of 7 .Therefore, it is true for n=1

We suppose that it is true for n=k

Then P(k)= is a multiple of 7.

We shall prove that it is true for n=k+1

P(k+1)= is a multiple of 7

LHS=

=

=

=

=  because is a multiple of 7 therefore

=

P(k+1) is a multiple of 7.

Therefore, P(n) is true for all natural numbers belongs to N.