Question

find the middle term of A.P 19,16,13,10.......-53? ​

Answer 1

Answer:

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Step-by-step explanation:

a = 19

d = 16-19= -3

an = -53

a+(n-1)d = -53

19+(n-1)-3 = -53

(n-1) = -72/-3

n =24+1 = 25

middle term = 25+1/2 = 26/2 = 13

therefore,a+12d = 19-36 = -17

here is your answer

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Answer 2

Given : AP  19,16,13,10.......-53

To find : Middle term

Solution:

Lets firs find total number of term

a = first term = 19

last term = - 53

d = 16 - 19 = - 3

nth term = a + (n-1)d

=> -53 = 19 + (n-1)(-3)

=> -72 =  (n-1)(-3)

=> 24 = n - 1

=> n = 25

there are 25 terms

so middle term = ( 1 + 25)/2 = 13 th term

13th term = a + (13-1)d

=> middle term = 19 + 12 * (-3)

=> middle term = 19 - 36

=> middle term = - 17

-17 will be middle term    

a Tip :

if number of terms are odd then

middle term  =  ( first term + last term)/2 = (19 - 53)/2 = -17

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