Question

Prove that no matters what the real numbers A and B are the pattern of number but an A+ nb is always an a.p. what is the common difference what's the sum of first 20 terms

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Answer 1

Answer:

Here's your answer!

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

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