Question

The 4th term of an A.P is twice its 8th term. If it's 6th term is -8. Find the sum of it first 20 terms.

pls help me solve this​

Answer 1

Answer:

- 280.

Step-by-step explanation:

From the properties of AP.

• nth term = a + ( n - 1 )d
• Sum of first n terms = ( n / 2 ){ 2a + ( n - 1 )d }

* where a is the first term, d is the common difference between the terms.

Let the first term of this AP be a and common difference between the terms be d.

Given,

2 x 4th term = 8th term

= > 2[ a + ( 4 - 1 )d] = [ a + ( 8 - 1 )d ]

= > 2a + 6d = a + 7d

= > a - d = 0

= > a = d

Also,

= > 6th term = - 8

= > a + 5d = - 8

= > a + 5a = - 8

= > 6a = - 8

= > a = - 4 / 3 = d

Therefore,

= > Sum of first 20 terms

= > ( 20 / 2 ) [ 2( - 4 / 3 ) + 19( - 4 / 3 )

= > 10[ 21( - 4 / 3 ) ]

= > - 10 x 7 x 4

= > - 280

Sum of 20 terms is - 280.