Question

The middle most term of AP: -7,-3,...-49 ?

Answer 1

We have to find the middle most term of arithmetic progression; -7, -3, 1, .... 49

solution : first term of given Ap, a = -7

Common difference, d = -3 - (-7) = -3 + 7 = 4

nth term, Tn = 49

Using formula, Tn = a + (n - 1)d

⇒49 = -7 + (n - 1) × 4

⇒49 + 7 = 4(n - 1)

⇒56 = 4(n - 1)

⇒14 = n - 1

⇒n = 15 (odd)

So middle term must be (n + 1)/2 = 8th term

now 8th term = a + (8 - 1)d = a + 7d

= -7 + 7 × 4 = -7 + 28 = 21

Therefore the middle most term of given Ap is 21.

Answer 2

Answer:

an=a+(n-1)

-49=-7+(n-1)4

-49=-7+4n-4

-49+7+4=4n

-49+11=3n

n=38/3