Question

Find the sum of the first 70 terms of the sequence

–6, –3, 0, 3, 6, ...


a. 6824

c. 6826

b. 6825

d. 6827


Please select the best answer from the choices provided


A
B
C
D

Answer 1

b.

6825

Explanation:

Answer 2

Option (b) is correct.

The sum of the first 70 terms of the sequence –6, –3, 0, 3, 6, ... is 6825.

Explanation:

Consider the given sequence, –6, –3, 0, 3, 6, ...

We have to find the sum of the first 70 terms of the sequence –6, –3, 0, 3, 6, ...

Here,
`a_1=-6,a_2=-3,a_3=0` and so on.

First find the difference between the terms,

`a_2-a_1=-3+6=3`

`a_3-a_2=0+3=3`

Since, the difference between the terms is constant,Hence, the given sequence is an Arithmetic sequence.

For a given A.P. with n terms having a as first term and d be the common difference the sum
`S_n` is given by,

`S_n=(n)/(2)(2a+(n-1)d)`

Here, a = -6 , n = 70 , d = 3 ,

Substitute , we get,

`S_(70)=(70)/(2)(2(-6)+(70-1)3)`

`S_(70)=(70)/(2)(2(-6)+(69)3)`

`S_(70)=(70)/(2)(-12+207)`

`S_(70)=(70)/(2)(195)`

`S_(70)=35 * 195`

`S_(70)=6825`

Thus, the sum of the first 70 terms of the sequence –6, –3, 0, 3, 6, ... is 6825.

Option (b) is correct.