`x_(n)` is the `n^(th)` term of an arithmetic sequence (common difference is not zero). If `x_(a), x_(b), x_(c),…..` is án arithmetic sequence, prove that a, b, c,….. is an arithmetic sequence.

The n^(th) term of an arithmetic sequence is a_n =5-6n.Find its sum of n terms?

10^(th) term of an arithmetic sequence is 82 , If its common difference is 8 , find the position of the term 250 in the sequence.

The sum of first n terms of an arithmetic sequence is n^2+2n Find the common difference.

Write the arithmetic sequence with first term 2 and common difference 3.

For the arithmetic sequence 6,12,18. What is the common difference?

The second term of an arithmetic sequence is 8 and the common difference is 3. Write the sequence?

90 is the term of the arithmetic sequence having common difference 3. Is 2000 term of this sequence? Why?

The common difference of the arithmetic sequence 15, 14, 13, 12,......is 14-15=-1. First term of the sequence is 15 and the 15^(th) term is 15 + 14 xx-1= 15-14=1 . Similarly the 4^(th) term is 12 and the 12^(th) term is 4. Its 16^(th) term is x_16 = 15 + 15xx-1= 15-15 = 0 . So the sum of the first 31 terms is also zero. That is if then n^(th) term of an arithmetic sequence with common difference -1 is m, then the m^(th) term is n and the (m + n)^(th) term is zero. 7^(th) term of an arithmetic sequence is 10 and the 10^(th) term is 7. What is the common difference?

Find the 20^(th) term of an arithmetic sequence if its 6^(th) term is 14 and 14^(th) term is 6.

Algebraic expressions of an arithmetic sequence is 5n+6 . Write the sequence.