Question

the 13th term of so is four its3rd term. if it's fifth term is 16 then find the sum of its first ten terms

Answer 1

Given, 13th term is 4 its 3rd term.

        =  a + 12d = 4(a+2d)

          4d = 3a             ---------------- (1)


Given, 5th term is 16

           =    a+4d = 16  (In (1) 4d = 3a)

            =   a + 3a = 16

           a = 4

Substitute a=4 in (1), we get d = 3


We should calculate sum of 1st 10 terms = n/2(2a+(n-1)d)

                                                                   = 10/2(2a+9d)

                                                                   = 5(8+27)
                      
                                                                   = 175.


Hope this helps!