Question

Find the number of terms in an
a.p. whose first term and 6th term are 12 and 8 respectively and sum of all terms is 120.

Answer 1

Hi,

Let a and d are first term and

common difference of an A.P

According to the problem given,

a1 = a = 12----( 1 )

a6 = 8

a + 5d = 8 ---( 2 )

Put ( 1 ) in equation ( 2 ) ,

12 + 5d = 8

5d = 8 - 12

5d = -4

d = -4/5

Now ,

a = 12 , d = -4/5,

Let the number of terms = n

Sn = 120

n/2 [ 2a + ( n -1 )d ] = 120

n/2 [ 2×12 + ( n - 1 )( -4/5 ) ] = 120

4n/2 [ 6 + ( n - 1 ) ( -1/5 ) ] = 120

2n [ 30 -n + 1 ]/5 = 120

n ( 31 - n ) = 120 × ( 5/2 )

31n - n² = 300

n² - 31n + 300 = 0


Plz , verify the question again there is

error in the data.