Question

Prove that no matter what the real numbers a and b are,the sequence with nth term a+nb is always an A.P. What is the common difference?​

Answer 1

Step-by-step explanation:

Given the sequence which is defined by.

a

n

=a+nb.....eq(1)

and we know that nth term of an A.p is given by

a

n

=a

1

+(n−1)d

which can also be written as

a

n

=a

1

−d+nd.....eq(2)

comparing eq(1) and eq(2) we get

common difference is

d=b (by comparing coefficients of n)

and

a

1

−d=a

by putting value of d=b in above equation we get

a

1

−b=a

⟹a

1

=a+b (first term of A.P)

hence if a and b are real numbers this sequence form an A.P with first term a

1

=a+b

and have a common difference d=b