Question

*For 10th grade*
(Q) Find the middle term of the A.P 10,7,4.....(-62)

Answer 1

10 , 7 , 4 , ...... , ( -62 ) are in A.P

first term = a = 10

common difference = d = a3 - a2 = 4 - 7 = -3

last term = n th term = an = l = - 62

we know that ,

a + ( n - 1 ) d = l

put above values in the formula,

10 + ( n - 1 ) ( - 3 ) = -62

⇒ ( n- 1 ) ( -3 ) = -62 - 10

⇒ ( n - 1 ) ( - 3 ) = - 72

⇒ ( n - 1) = ( - 72 ) / ( - 3 )

⇒ n - 1 = 24

∴ n= 24 +1

n = 25

ii ) number of terms in given A. P = n= 25 ( odd )

middle term = ( n+ 1 ) /2 th term

= (25 +1) / 2 th term

= 26 /2 th term

= 13 th term

iii) a = 10 , d= -3 , n= 13 ,

a13 = ?

a13 = a + 12d

= 10 + 12 × ( -3 )

= 10 - 36

= -26

∴ middle term in given A. P = -26