Sue Pemberton Solutions for Chapter: Series, Exercise 6: EXERCISE 6C

The first two terms in an arithmetic progression are $146$ and $139$. The last term is $-43$. Find the sum of all the terms in this progression.

The first two terms in an arithmetic progression are $2$ and $9$. The last term in the progression is the only number that is greater than $150$. Find the sum of all the terms in the progression.

The first term of an arithmetic progression is $15$ and the last term is $27$. The sum of the first five terms is $79$. Find the number of terms in this progression.

 Find the sum of all the integers between $100$ and $300$ that are multiples of $7$.

The first term of an arithmetic progression is $2$ and the ${11}^{\mathrm{th}}$ term is $17$. The sum of all the terms in the progression is $500$. Find the number of terms in the progression.

The sixth term of an arithmetic progression is $-3$ and the sum of the first ten terms is $-10$. Given that the ${\mathrm{n}}^{\mathrm{th}}$ term of this progression is $-59$, find the value of $\mathrm{n}$.
 

An arithmetic sequence has first term a and common difference d. The sum of first 20 terms is 7 times the sum of the first five terms. Find the 65th term in terms of a.

The sum of the digits in the number $67$ is $13 (\mathrm{as} 6+7=3)$. Find the sum of the digits of the integers from $1 \mathrm{to} 99$.