Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | January | Q#6
An arithmetic sequence has first term a and common difference d.
The sum of the first 10 terms of the sequence is 162.
a. Show that 10a + 45d =162
Given also that the sixth term of the sequence is 17,
b. write down a second equation in a and d,
c. find the value of a and the value of d.
We are given following data of Arithmetic Series;
Expression for the sum of number of terms in the Arithmetic Progression (A.P) is:
Expression for the general term in the Arithmetic Progression (A.P) is:
Therefore, for given 6th term we can write equation as;
We have found two equations in terms of a and d in (a).
We can simultaneously solve these two equations.
We can find expression for a from second equation;
Substitute this expression of a in first equation;
Substituting in any of the above two equations yields ‘a’;