Write the Properties of A.P.

1.	Write the Properties of A.P.
Answer» (A) For any real numbers a and b, the sequence whose nth term is a_n = an + b is always an A.P. with common difference ‘a’ (i.e. coefficient of term containing n) (B) If any nth term of sequence is a linear expression in n then the given sequence is an A.P. (C) If a constant term is added to or subtracted from each term of an A.P. then the resulting sequence is also an A.P. with the same common difference. (D) If each term of a given A.P. is multiplied or divided by a non-zero constant K, then the resulting sequence is also an A.P. with common difference Kd or......... respectively. Where d is the common difference of the given A.P. (E) In a finite A.P. the sum of the terms equidistant from the beginning and end is always same and is equal to the sum of 1st and last term. (F) If three numbers a,b,c are in A.P., then 2b = a + c.

Answer»

(A) For any real numbers a and b, the sequence whose nth term is a_n = an + b is always an A.P. with common difference ‘a’ (i.e. coefficient of term containing n)

(B) If any nth term of sequence is a linear expression in n then the given sequence is an A.P.

(C) If a constant term is added to or subtracted from each term of an A.P. then the resulting sequence is also an A.P. with the same common difference.

(D) If each term of a given A.P. is multiplied or divided by a non-zero constant K, then the resulting sequence is also an A.P. with common difference Kd or......... respectively. Where d is the common difference of the given A.P.

(E) In a finite A.P. the sum of the terms equidistant from the beginning and end is always same and is equal to the sum of 1st and last term.

(F) If three numbers a,b,c are in A.P., then 2b = a + c.

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