Question

find the sum of the first

20 terms of an ap in which the third term is 7 and the seventh term is 2more then thrice its term​

Answer 1

a3 or a+2d= 7 -1 , n= 20

a7= 2+ 3 (a7)

a+6d= 2+3(a+6d)

a+6d= 2+ 3a+ 18d

a+6d-3a-18d = 2

-2a - 12d = 2. ( divide by2

-a -6d =1 -2

adding eq1 and 2

a+2d=7

-a-6d=1

we get-4d =8

d=-2

put in eq1

a+2d=7

a+2×-2=7

a-4=7

a=11

S=n/2+(n-)d

S=20/2+(20-1)-2

S= 10+19×-2

S= 10- 38

S= -28