Question

the sum of first 5 terms of an ap is 55 the 4th term of the sequence is 5 more than the sum of the next 2 terms then find ap​

Answer 1

Answer:

a₁=13

a₂=a+d=12

a₃=a+2d=11

a₄=a+3d=10

a₅=a+4d=9

a₆=a+5d=8

a₇=a+6d=9

Step-by-step explanation:

S₅=55

5/2(2a+4d)=55

2a+4d=22

a+2d=11 --------------------(i)

a₆+a₇=a₄+5

a+5d+a+6d=a+3d+5

2a+11d=a+3d+5

a+8d=5 --------------------(ii)

Subtracting (ii) from (i),

 a+2d=11

 -

 a+8d=5

------------------

    -6d=6

d= -1

In (i),

a+2d=11

a+ 2*-1=11

a=11+2

a=13

So, the AP is:

a₁=13

a₂=a+d=12

a₃=a+2d=11

a₄=a+3d=10

a₅=a+4d=9

a₆=a+5d=8

a₇=a+6d=9