Question

Find the value of the middle most term(s) of the A.P :-11, -7, -3,...............,49

Answer 1

Answer:

17

Step-by-step explanation:

We have :-

a1 = -11

a2 = -7

a3 = -3

an = 49

Find d first,

d = a2 - a1

d = -7-(-11)

d = -7+11 = 4

Now, find n:-

an = a+(n-1)d

Putting the values, we get :-

49 = -11 + (n-1)4

49 = - 11 4n - 4

49 = 4n - 4 - 11

49 = 4n - 15

49+15 = 4n

64 = 4n

So, n = 16

It is even, so applying the formula for the median , when the term is even, we get:-

(n+1)/2th term + n/2 th term

Put n = 16

so , we get n/2 = 16/2 = 8th term

Now , putting in an = a+(n-1)d

an = -11 + (n-1)4

an = -11 + (8-1)4

an = -11 +(7)4

an = -11+28

an = 17

So, 17 is the required answer....

Answer 2

Answer:

17

Step-by-step explanation:

Here,

We have :-

a1 = -11

a2 = -7

a3 = -3

an = 49

Finding d first,we get

d = a2 - a1

d = -7-(-11)

d = -7+11 = 4

Now, find n:-

an = a+(n-1)d

Putting the values, we get :-

49 = -11 + (n-1)4

49 = - 11 4n - 4

49 = 4n - 4 - 11

49 = 4n - 15

49+15 = 4n

64 = 4n

So, n = 16

Now,

Put n = 16

so , we get n/2 = 16/2 = 8th term

Now , putting in an = a+(n-1)d

an = -11 + (n-1)4

an = -11 + (8-1)4

an = -11 +(7)4

an = -11+28

an = 17

So, 17 is your answer....