Question

Find the first three terms of the arithmetic series in which a1 = 2, an = -25, and Sn = -115.

Answer 1

Step-by-step explanation:

Let first three terms be

a , a + d , a + 2d

an = a + ( n - 1 )d

- 25 = 2 + ( n - 1 )d

- 25 - 2 = ( n - 1 )d

- 27 ÷ ( n - 1 ) = d ...... ( 1 )

Sn = n ÷ 2 [ a + l ]

- 115 = n ÷ 2 [ 2 + ( - 25 ) ]

- 115 = n ÷ 2 [ 2 - 25 ]

- 115 × 2 = n ( - 23 )

- 230 ÷ - 23 = n

n = 10 ........ ( 2 )

Put n = 10 in equation 1 :

d = - 27 ÷ ( n - 1 )

d = - 27 ÷ ( 10 - 1 )

d = - 27 ÷ 9

d = - 3

Therefore ,

a = 2.

a + d = 2 + ( - 3 ) = 2 - 3 = - 1.

a + 2d = 2 + 2 ( - 3 ) = 2 - 6 = - 4.

In ARITHMETIC PROGRESSION

2 , - 1 , - 4 ,...........