Question

The sum of 5th and 9th term of an ap is 26 and the 7th and 11tg term is 42 find the first 3 terms of AP

Answer 1

=> a5 = a + 4d

=> a9 = a + 8d

=> Sum of a5 and a9 = a + 4d + a + 8d

=> 26 = 2a + 12d

=> Dividing it by 2

=> 13 = a + 6d - equation ( 1 )

=> a7 = a + 6d

=> a11 = a + 10d

=> Sum of a7 and a11 = a + 6d + a + 10d

=> 42 = 2a + 16d

=> Dividing by it 2

=> 21 = a + 8d - equation ( 2 )

=> From 1 and 2

=> a + 6d = 13

=> a + 8d = 21

=> -2d = -8

=> d = 4

=> a + 6 ( 4 ) = 13

=> a = 13 - 23 = -11

=> AP = a , a + d , a + 2d

=> AP = -11 , -7 , -3

ANS => -11 ,-7 , -3

I hope this will help you dear..

Always stay safe and stay healthy..

Answer 2

Solution:-

=> The sum of 5th and 9th of AP is 26

Formula

=> Tₙ = a + ( n - 1 ) d

According to question we can write

=> a + ( 5 - 1 )d + a + ( 9 - 1 )d = 26

=> a + 4d + a + 8d = 26

=> 2a + 12d = 26

=> a + 6d = 13 ........(i)eq

Again given Sum of 11th and 7th term is 42

=> a + ( 7 - 1 )d + a + ( 11 - 1 )d = 42

=> a + 6d + a + 10d = 42

=> 2a + 16d = 42

=> a + 8d = 21 .......( ii ) eq

Now subtract (ii) from (i)

=> a + 6d - a - 8d = 13 - 21

=> -2d = -8

=> d = 4

Now put the value of d on (i) eq

=> a + 6d = 13

=> a + 6 × 4 = 13

=> a + 24 = 13

=> a = 13 - 24

=> a = - 11

We have to find 3rd term

T₃ = a + ( 3 - 1 )d

=> T₃ = -11 + 2 × 4

=> T₃ = - 11 + 8

=> T₃ = -3