Question

The sum of the first 3 terms in an AP is 51 and that of the last 3 is 99 if the ap has 11 terms what is the arithmetic mean of the middle 3 terms?

Answer 1

Let the first terms of the AP be a

common difference of the AP be d

then,

Acccording to question

a+a+d+a+2d=51

3a+3d=51

a+d=17..…...i)

a+10d+a+9d+a+8d=99

3a+27d=99

a+9d=33......ii)

now, subtract I) from ii)

8d=16

d=2

putting this value of d,in ii) we get

a=33-18

a=15

AP, will be,15,17,19......

now, middle term of this series=11/2=5.5,=6(approx)

middle term=a+5d=15+5×2=25

{hope it helps you}

Answer 2

Answer:

Step-by-step explanation:

Let the first terms of the AP be a

common difference of the AP be d

then,

Acccording to question

a+a+d+a+2d=51

3a+3d=51

a+d=17..…...i)

a+10d+a+9d+a+8d=99

3a+27d=99

a+9d=33......ii)

now, subtract I) from ii)

8d=16

d=2

putting this value of d,in ii) we get

a=33-18

a=15

AP, will be,15,17,19......

now, middle term of this series=11/2=5.5,=6(approx)

middle term=a+5d=15+5×2=25

{hope it helps you}