Find the sum of the 10 terms between 5 and 62 which together

Find the sum of the 10 terms between 5 and 62 which together form an A.P.

Solution

Method 1:       sum of n terms of an AP = [first term+last term]x n/2

                        In this case the sum of 10 terms    = [5+62]x5= 335

Method 2: 1st term =a[1]=5

                 10th term a[10]=62

If d is the common difference, then

                                a[10]= a[1]+ (10-1)d

                                      62= 5+9d

so                                    d =19/3

Sum of the first 10 terms = [2a+9d]x5

                                            = 67x5=335