Question

If the sum of the first 14 terms of an A.P is 1050 and it's first term is 10, find the 20th term.

Answer 1

Hey Mate!

Given,

Sum of first 14 terms = 1050

S14 = n/2 ( 2a + ( n - 1) d

S14 = 14/2 ( 2 (10) + 13d)

1050 = 7 ( 20 + 13d)

1050/7 = 20 + 13d

150 = 20 + 13d

150 - 20 = 13d

130 = 13d

d = 130/13

d = 10

20th term = a + 19d

= 10 + 190

= 200


HOPE THIS HELPS U...

Answer 2

Solution:-

Given:-

S14 = 14/2 [ 2a + ( 14 - 1)d ] = 1050.

a = First Term = 10.

To Find :-

a20 = ?

Find:-

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

=) s14 = 14/2 [ 2(10) + ( 14 - 1)d ]

=) 1050 = 7 [ 20 + 13d ]

=) 1050/7 = 20 + 13d

=) 150 - 20 = 13d

=) d = 130/13

=) d = 10.

Now,

a20 = a + 19d

=) a20 = 10 + 19×10

=) a20 = 10 + 190

=) a20 = 200.