Question

The sum of 4th and 8th terms of an ap is 24 and the sum of 6th and 10th terms of the same ap is 34 find the first three terms of the ap

Answer 1

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Answer 2

Answer:

a = - 13

d = 5 / 2

Step-by-step explanation:

Let the first term a and common difference be d.

We know :

t_n = a + ( n - 1 ) d

t_4 = a + 3 d

t_8 = a + 7 d

We have given :

t_4 + t_8 = 24

2 a + 10 d = 24

a + 5 d = 12

a = 12 - 5 d ....( i )

t_6 = a + 5 d

t_10 = a + 9 d

: t_6 + t_10 = 34

2 a + 14 d = 34

a + 7 d = 17

a = 17 - 7 d ... ( ii )

From ( i ) and  ( ii )

12 - 5 d = 17 - 7 d

7 d - 5 d = 17 - 12

2 d = 5

d = 5 / 2

We have :

a = 12 - 5 / 2

a = 19 / 2

a = - 13

d = 5 / 2