Find the middle term of the AP : 5 , 2 , -1 , - 4 ,,..,- 31

-13

Explanation:

Nth term will be:

Tn = a+(n-1)d

where,

Tn = 31

a = first term = 5

d = common difference= 2-5 = -3

Tn = a+(n-1)d

-31 = 5+(n-1)-3

-31 = 5-3n+3

Collect like terms

-31-5-3= -3n

-39 = -3n

n = -39/-3

n = 13

Middle term = (n+1)/2

= (13+1)/2

= 14/2

= 7

7th term will be

= a + (n-1)d

= a + (7-1)d

= a+6d

= 5 + 6(-3)

= 5-18

= -13

Therefore, the middle term is -13.

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