algebra and trigonometry

Question

The nth term of a certain series is given by A+B if the first term is 5 and the second term is 10, find
a) the value of A and B
b) the sum of the first ten terms of the series.

Answer 1

The information seems to be insufficient. 

The last term being A+B, there has to be a relation between A+B and the terms in the series.

 

 

The series is an Arithmetic Progression and is resolved as below:

 

 

Sum to first 10 terms is given by:

 

Sn = n [2 A1 + (n-1) D)

        2 

 

 = 10 [ 2*5 + (10-1) 5]      A1 - ist term in the series, ie 5

     2

                                        n - number of terms -- 10  (since we are asked for the sum to 10 terms)

 

                                        D - common difference  = 10-5 = 5 (1st term is 5 and 2nd term is 10 ) -- given

 

= 5 * [10 + 9*5] = 5 * 55 = 275