Complicated arithmetic series and it's sum of first n terms

The sum of an infinite geometric series is 162 and the sum of its first n terms is 160. If the inverse of its common ratio is an integer, then which of the following is not a possible first term? 108 b. 144 c. 160 d. none of these

The sum of an infinite geometric series is 162 and the sum of its first n terms is 160. If the inverse of its common ratio is an integer, then which of the following is not a possible first term? 108 b. 144 c. 160 d. none of these

If the sum of the first 100 terms of an arithmetic progression is -1 and the sum of the even terms is 1, then the 100^("th") term of the arithmetic progression is

The sum of the first n terms of a series is 31, and the sum of the first n - 1 terms of the series is 20. What is the value of nth terms in the series?

The first term of an arithmetic progression is 1 and the sum of the first nine terms equal to 369 . The first and the ninth term of a geometric progression coincide with the first and the ninth term of the arithmetic progression. Find the seventh term of the geometric progression.

The first term of an arithmetic progression is 1 and the sum of the first nine terms equal to 369 . The first and the ninth term of a geometric progression coincide with the first and the ninth term of the arithmetic progression. Find the seventh term of the geometric progression.

Find the sum of first n terms and the sum of first 5 terms of the geometric series 1 + 2/3 + 4/9 +dotdotdot

If the sum of the first 4 terms of an arithmetic progression is p, the sum of the first 8 terms is q and the sum of the first 12 terms is r, express 3p+r in terms of q.

If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.

If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.