arithmetic progression help (1 Viewer)

[bananarama69]

please help if you can.

the sum of the first and fourth terms of an AP is 16 and the sum of the third and 8th terms is 4. Find the sum of the first 10 terms.

 

[Trebla]

please help if you can.

the sum of the first and fourth terms of an AP is 16 and the sum of the third and 8th terms is 4. Find the sum of the first 10 terms.

The first term is: 'a'
The third term is: 'a + 2d'
The fourth term is: 'a + 3d'
The eighth term is: 'a + 7d'

Sum of first and fourth terms is 16
=> a + a + 3d = 16
=> 2a + 3d = 16

Sum of third and eighth terms is 4
=> a + 2d + a + 7d = 4
=> 2a + 9d = 4

Solving the two simultaneous equations:
d = - 2
a = 11

So the sum of the first 10 terms are:
S = (10/2) (2(11) + 9(-2))
= 20