In an arithmetic sequence `n^(th)` term is m and `m^(th)` term is n, prove that its common difference is -1.

Consider an arithmetic sequence whose m^(th) term is 'n' and n^(th) term is 'm . i)Find the common difference of the sequence. ii) Prove that (m+n+p)th term of the sequence is -p

Consider an arithmetic sequence whose 7^(th) term is 34 and 15^(th) term is 66. Find the common difference.

The 25^(th) term of an arithmetic sequence is 140 and the 27^(th) term is 166 . What is its common difference? What is its 35^(th) term?

The 5^(th) term of an arithmetic sequence is 38 and 8^(th) term is 62. What is the common difference in the sequence?

23^(rd) term of an arithmetic sequence is 32. 35^(th) term is 104. Then what is the common difference?

In an arithmetic sequence, m times the n^(th) term is equal to n times the m^(th) term. Prove that. its first term and common difference are equal.

Consider an arithmetic sequence whose 7^(th) term is 34 and 15^(th) term is 66. Find the 20^(th) term.

23^(rd) term of an arithmetic sequence is 32. 35^(th) term is 104. Then a) What is the common difference? b) Which is the middle term of first 35 terms of this sequence? c) Find the sum of first 35 terms of this sequence.

Read the following Passage. Understand the Mathematical concept in it and answer the questions that follow. Each question carries 1 score. The common difference of the arithmetic sequence 15,14,13,12,...... is 14-15=-1 . First terms of the sequence is 15 and the 15th term is 15+14x-1=15-14=1 . Similarly the 4th term is 12 and the 12^(th) term is 4. Its 16th term is, x_(16)=15+15x-1=15-15=0 . So the sum of the first 31 terms is also zero. that is if the n^(th) is m, then the mth term is n and the (m+n)^(th) term is zero. Seventh term of an arithmetic sequence is 10 and the 10^(th) term is 7. What is the common difference?

The ratio between the 4^(th) term and 8^(th) term of an arithmetic sequence is 5: 11 . " "10^(th) term of this sequence is 56 i) What is the common difference of this sequence? ii) Find the 16^(th) term. iii) Find the sum of first 25 terms.