If the mth term of an A. P. is and nth term is then show that its (mn)^th term is 1. 

Find the sum of n terms of the series 

The ratio of the sums of the first m and first n terms of an A. P. is m₂: n₂. Show that the ratio of its mth and nth terms is (2m−1):(2n−1). 

In an AP, if the common difference (d) = –4, and the seventh term (a₇) is 4, then find the first term.

355.

Find the sum of first 8 multiples of 3.

The sum of four consecutive numbers in an AP is 32 and the ratio of the product of the first and the last term to the product of two middle terms is 7 : 15. Find the numbers.

The common difference of AP $\frac{1}{3q}. \frac{1-6q}{3q}, \frac{1-12q}{3q}, ........ is;$1 1 6q 1 12q, , 3q 3q 3q
... is:

• q

• -q

• -2

• 2

How many three-digit natural numbers are divisible by 7?

The sum of first n terms of an AP is 3n² + 4n. Find the 25th term of this AP.

Find the number of terms of the AP -12, -9, -6,... 12. If 1 is added toeach term of this AP, then find the sum of all terms of the AP thusobtained.