Question

find the middle term of the AP 213,205,197...37

Answer 1

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Answer 2

ANSWER:

Given

first term ( a ) = 213

Common difference ( d ) = t2 - t1 = 205 - 213 = - 8

Last term = 37

37 = a + (n - 1)d

37 = 213 + (n - 1)(- 8)

37 = 213 - 8n + 8

37 = 221 - 8n

8n = 221 - 37

8n = 184

n = 184/8 = 23

TO FIND:

Middle term of A.P.

$\small{ \sf{ t_{ \frac{n}{2} } = a + ( \frac{n}{2} - 1)d }}$

tn/2 = 213 + ( 23/2 - 1 )(-8)

t23/2 = 213 + (11.5 - 1)(-8)

11.5 approximately = 12

t12 = 213 + (12 - 1)(-8)

t12 = 213 + 11(-8) = 212 - 88

t12 = 125

Hence middle term of A.P. = t12 = 125