Find all sequences which are simultaneously A.P. and G.P.

The nth term of a sequence is 8 -5n. Show that the sequence is an A.P.

The sum of three numbers which are consecutive terms of an A.P. is 21. If the second number is reduced by 1 and the third is increased by 1 we obtain three consecutive terms of a G.P. Find the numbers.

p : · If nth term of a sequence _is linear then sequence is in A.P. Converse of statement p is

In a sequence of 21 terms the first 11 terms are in A.P. with common difference 2. and the last 11 terms are in G.P. with common ratio 2. If the middle tem of the A.P. is equal to the middle term of the G.P., then the middle term of the entire sequence is

If nth term of a sequences is 4n^2+1, find the sequence. Is this sequences at A.P.?

The nth term of a sequence is 3n-2 is the sequence an A.P.? If so, find its 10th term.

In a set of four numbers, the first three are in G.P. and the last three are in A.P. with difference 6. If the first number is the same as the fourth, find the four numbers.

If a,b,c,d are distinct positive then a^n/b^ngtc^n/d^n for all epsilon N if a,b,c,d are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

If a,b,c are in A.P. as well as in G.P. then

Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.