Prove that if a constant is added to or subtracted from each terms of an AP; then the resulting sequence is also an AP with the same common difference.

(i) If a constant is added to or substracted from each terms of an AP; then the resulting sequence is also an AP with the same common difference.

Each term of an A.P. is doubled,. Is the resulting sequence also an A.P.? If it is write its first term, common difference and nth term.

Each term of an A.P. is doubled. Is the resulting sequence also an A.P. ? If it is, write its first term common difference and nth term.

Each term of an A.P. is doubled. Is the resulting sequence also an A.P.? If it is, write its first term, common difference and n^(th) term.

The 11th term of an A.P. is 60 less than the 31st term of an A.P. . Find the common difference.

(ii)If each terms of a given AP,is multiplied or devided by a non zero constant k; then the resulting sequence is an AP with common difference kd or (d)/(k); where d is the common difference of the given AP.

(iii) If each terms of the AP is raised to some power; the resulting sequence also forms an AP

Similarly subtract a fixed number from each and every term of A.P. Write the resulting numbers as a list.

Show that the sequence defined by a_(n)=4n+5 is an AP .Also,find its common difference.

If 16th term is 16 more than the 12th term of an AP then find the common difference of the AP