Question

d=5, s9= 75, find a and a9

Answer 1

d = 5

S9 = 75

By applying the formula

Sn = n / 2 + ( 2a + ( n - 1 ) × d

75 = 9 / 2 + (2a + ( 9 - 1 ) × 5

75 = 9 / 2 + ( 2a + 40 )

75 × 2 / 9 = 2a + 40

50 / 3 = 2a + 40

50 / 3 - 40 / 1 = 2a

by taking LCM we will get

- 70 / 3 = 2a

a = - 70 / 3 × 2

a = - 35 / 3.

a9 = a + 8d

= -35 / 3 + 8 × 5

= - 35 / 3 + 40

= -35 + 120 / 3

= 95 / 3.

Hope It Helps you !!

Dear!

Answer 2

Answer:

S9 = 9/2 ( 2a + ( 9-1) d)

=> S9 = 9/2 ( 2a + 8d )

=> S9 = 9/2 ( 2a + 8 × 5 )

=> S9 = 9/2 ( 2a + 40 )

=> S9 = 9/2 × 2 ( a + 20)

=> S9 = 9 ( a + 20 )

=> 75 = 9 ( a + 20 )

=> 75/9 = a + 20

=> a = (75/9) -20

=> a = (25/3) - 20

=> a = (25-60)/3

=> a = -35/3

a9 = a + (9-1)d

= (-35/3) + 8d

= (-35/3) + 8×5

= (-35/3) + 40

= (-35+120)/3

= 85/3