Question

Some one help me with the 4th one and please give me step by step explanation

Answer 1

Answer:

-340

Step-by-step explanation:

Let a be the first term and let d be the common difference.

The n-th term is then:   a + (n-1)d

Given 6th term is -8

=> a + 5d = -8        ... (1)

Given 14th term is twice the 8th term

=> a + 13d = 2 × ( a + 7d )

=> a + 13d = 2a + 14d

=> a + d = 0        ... (2)

Putting a = -d (from equation (2)) into equation (1) gives

-d + 5d = -8  =>  4d = -8  =>  d = -2

Also a = -d, so a = 2

The sum of the first n terms is given by

na + [ n(n-1)/2 ] × d

So the sum of the first 20 terms is

20a + [ (20)(19)/2 ] × d

= 20a + 190d

= 20×2 + 190×(-2)

= 40 - 380

= -340

Answer 2

Answer: refer to the attachment below.