Question

Find the middle term of AP -6,-2,2....58

Answer 1

Answer:

26

Step-by-step explanation:

First term (a) = -6

Common difference (d) i.e term 2 - term 1 = -2+6 = 4

Last term (l) = 58

To find the number of terms in the A.P

We will use the formula - l = a+(n-1)d

Substituting the values we get

58 = -6+(n-1)4

58 = -6+4n-4

58+6+4 = 4n

68 = 4n

68/4 = n

17 = n

Therefore the number of terms is 17

From the number of terms we can infer that the 9th term is the middle term of the A.P

So therefore to find the 9th term,let's use the formula - t9 = a+(n-1)d

where, a = -6 , d = 4 , t9 = t and n = 9

Substituting the values we get

t = -6+(9-1)4

t = -6+36-4

t = 26

Therefore the middle term of the A.P -6,-2,2.....58 is 26