Given d = 5, S" 75, find a and a9.

1.	Given d = 5, S" 75, find a and a9.
Answer» 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.

Answer»

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.

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