Question

the sum of the 6 terms of AP is 345 and the difference between first term and last term is 55 find the AP

Answer 1

Let the six terms be a a+d a+2d a+3d a+4d a+5d    ------ (*)

Given, a+a+d+a+2d+a+3d+a+4d+a+5d = 345

           6a + 15d = 345     ------------------   (1)


Given, a + 5d - a = 55

            5d = 55

             d = 11.    ------------------- (2)


Substitute equation (2) in (1), we get


6a + 15(11) = 345

6a = 345 - 165

6a = 180

a = 30  ------------------ (3)

On Substituting d = 11 and a = 30 in (*) we get the AP values as

30,41,52,63,74,85.


Hope this helps!