Sequences and Series

An A.P. has first term 7 and common difference 3. Find the number of terms if the last term is 61 and also find the sum of all terms.

Insert 4 arithmetic means between 3 and 18. What is the third arithmetic mean and the sum of the four inserted means?

A bank deposit earns simple interest yearly. The amounts at the end of successive years form an A.P. with first term ₹10000 and common difference ₹500. Find the amount at the end of the 15th year and the amount at the end of 20 years.

A machine costs ₹15625 and depreciates by 20% each year. Find its value at the end of 5 years and also the common ratio of the yearly values.