Question

In an ap sum of 2nd and 5th term is 29 and sum of 3rd and 7th term is 20 then write the ap

Answer 1

Answer:

Given that:

◇ $\tt{a_{2} + a_{5} = 29}$

◇ $\tt{a_{3} + a_{7} = 20}$

=》 a + d + a + 4d = 29

=》 2a + 5d = 29

=》 2a = 29 - 5d ...(1)

=》 a + 2d + a + 6d = 20

=》 2a + 8d = 20

=》 2a = 20 - 8d ...(2)

(1) = (2)

=》 29 - 5d = 20 - 8d

=》 (-9) = 3d

=》 d = (-3)

2a = 29 - 5d

2a = 29 + 15

2a = 44

=》 a = 22

Arithmetic Progression : 22, 19, 16, ...

Answer 2

Answer : 22, 19, 16, 13..

Step-by-step explanation:

ATQ,

$\tt{a_2 + a_5 = 29}$

=> (a + d) + (a + 4d) =29

=> 2a + 5d=29..(1)

Also, As per next condition,

$\tt{a_3 + a_7 = 20}$

=> (a+2d) + (a + 6d) = 20

=> 2a + 8d = 20.. (2)

Subtracting eq. (2) from eq. (1)

2a+8d=20

- 2a+5d=29

__________

=> 3d = -9

d = -3

Substituting value of d in eq.(1)

2a + 5d = 29

2a - 15 = 29

2a = 44

a = 22

First term = 22

Second term = a + d = 22 - 3 = 19

Third term = 2nd term + d = 19 - 3 = 16

Forth term = 3rd term + d = 16 - 3 = 13

Therefore,

The A.P is 22, 19, 16, 13...