Question

The sum of six terms in an A.P is 75.The last term exceeds the first term by 15.Then the first term is

Answer 1

According to first condition,

S6 = 75

=> 6/2 [ 2a + (6-1)d] = 75

=> 3 [ 2a + 5d] = 75

=> 2a + 5d = 25 -------(1)


According to second condition,

T6 - T1 = 15

=> a + 5d - a = 15

=> 5d = 15

=> d = 3

On putting the value of d in equation 1, we get

2a + 5(3) = 25

=> 2a + 15 = 25

=> 2a = 10

=> a = 5

First term = 5

Answer 2

According to first condition,

S6 = 75

=> 6/2 [ 2a + (6-1)d] = 75

=> 3 [ 2a + 5d] = 75

=> 2a + 5d = 25 -------(1)

According to second condition,

T6 - T1 = 15

=> a + 5d - a = 15

=> 5d = 15

=> d = 3

On putting the value of d in equation 1, we get

2a + 5(3) = 25

=> 2a + 15 = 25

=> 2a = 10

=> a = 5

First term = 5