if the first term of an AP is 2. the sum of fiveth term is equal to 1/4 of the next five term. find the sum of first 30 term?

sum of first 5 terms S5 = 5/2[2+2+(5-1)d]

                                = 10+10d

Sum of first 10 terms S10 = 10/2[2+2+(10-1)d]

                                     =  20+45d

For calculation of sum of next five terms is S10-S5 = 10+35d

sum of first five terms = ¼ sum of next 5

10+10d = 1/4[10+ 35d]

40+40d=10+35d

5d = – 30

on simplification d = – 6

no sum of first thirty terms = 30/2[2+2+(30–1)(–6)]
                                       =15[4 – (29x6)]
                                        =15[ – 170]
                                        = – 2550

 

Thanks and regards,

Kushagra