Question

The sum of the 1st 9 terms of an arithmetic progression is 171 and the sum of the next 5 terms is 235. Find the (a) common difference (b) 1st term (c) sequence

Answer 1

Hi,

first term =3, common difference=4

Explanation:

Let's assume a the first term and r the common difference.

The sum of the 1st 9 terms of an arithmetic progression is 171:

`\displaystyle\ \sum_(i=1)^9\ u_i=\sum_(i=1)^9\ a+(i-1)*r=9*a+r*(8*9)/(2) \\\\9*a+36*r=171\\`

The sum of the next 5 terms is 235

`\displaystyle\ \sum_(i=10)^(14)\ u_i=\sum_(i=10)^(14)\ a+(i-1)*r=5*a+r*(5*22)/(2) \\\\5*a+55*r=235\\\\`

`\left\{\begin{array}ccc9*a+36*r&=&171&5&55\\5*a+55*r&=&235&-9&-36\\\end {array} \right.\\\\\\\left\{\begin{array}{ccc}-315*r&=&-1260\\315*a&=&945\\\end {array} \right.\\\\\\\left\{\begin{array}{ccc}r&=&4\\a&=&3\\\end {array} \right.\\\\`