Question

What is the value of this ?>>>>

Answer 1

1456

Explanation:

This is the sum of a geometric sequence

The n th term of a geometric sequence is

`a_(n)` = a
`(r)^(n-1)`

where a is the first term and r the common ratio

4
`(3)^(n-1)` ← is in this form

with a = 4 and r = 3

The sum to n terms of a geometric sequence is

`S_(n)` =
`(a(r^n-1))/(r-1)`, hence

`S_(6)` =
`(4(3^6-1))/(3-1)` =
`(4(729-1))/(2)` = 2 × 728 = 1456

Answer 2

option D is correct.

Explanation:

We need to find the value of

`\sum_(n=1)^(6) 4(3)^(n-1)`

Here value of n starts from 1 and goes on till 6

And we need to add the values of all the terms by putting value of n from 1 to 6

This can be written as:

`=4(3)^(1-1)+4(3)^(2-1)+4(3)^(3-1)+4(3)^(4-1)+4(3)^(5-1)+4(3)^(6-1) \\    Solving\\=4(3)^0+4(3)^1+4(3)^2+4(3)^3+4(3)^4+4(3)^5\\=4(1)+4(3)+4(9)+4(27)+4(81)+4(243)\\=4+12+36+108+324+972\\=1456`

So, option D is correct.