Question

If 3rd term is 7and 7th term is two more than thrice of its third term find s30

Answer 1

a3 = 7 = a+2d ..................(1)
a7 = 2+3(7) = 23 = a+6d .......…………(2)


(2)-(1) :-
a+6d-a-2d = 23-7
4d= 16
d=4 ……………………………………………(A)

from (1)
a= (-1)


s30 = n/2 (2a+d(n-1))
= 15((-2)+4(29)
= 15x144



s30 = 1710




hope this will help you : )

Answer 2

N th term of an A.P. is given by

$\textbf {a + (n-1) d}$

So

a₃= 7
a+2d = 7 ........(1)

a₇= 2+ 3(a₃)
a₇ = 23
a+6d = 23 .....(2)

Subtract (1) from (2)

4d = 16
d = 4

Put d=4 in (1)
so
a+ 2(4) = 7
a+ 8= 7
a= -1

$\textbf {Sum of Ap}$

n/2 ( 2a+ (n-1)d)

30/2(2(-1) + (29)4)
15 (-2+116)

15 × 114
→1710.