Question

Find the middle term of the A.P.6,13,20,.....216.

Answer 1

Given:-

first term(a) = 6

common difference(d) = 13 - 6 = 7

last term = 216

Tn = a + (n - 1)d

216 = 6 + (n - 1)7

216 = 6 + 7n - 7

216 = 7n - 1

7n = 217

n = 217/7

n = 31

So, there are 31 terms in an AP...

Middle term of an AP is given by:-

Middle term = (total terms + 1)/2

=> (31+1)/2

=> 32/2

=> 16th term.

a(16) = 6 + (16 - 1)7

=> 6 + (15)7

=> 6 + 105

=> 111.

Hence, Middle term or 16th of an AP is 111.

Answer 2

Answer:

Given:-

first term(a) = 6

common difference(d) = 13 - 6 = 7

last term = 216

Tn = a + (n - 1)d

216 = 6 + (n - 1)7

216 = 6 + 7n - 7

216 = 7n - 1

7n = 217

n = 217/7

n = 31

So, there are 31 terms in an AP...

Middle term of an AP is given by:-

Middle term = (total terms + 1)/2

=> (31+1)/2

=> 32/2

=> 16th term.

a(16) = 6 + (16 - 1)7

=> 6 + (15)7

=> 6 + 105

=> 111.

Hence, Middle term or 16th of an AP is 111.