Question

Evaluate !! look at photo please i need help

Answer 1

`Sum = 832`

Explanation:

Given

See attachment

Required

Evaluate

The expression can be expressed as:

`Sum = 2n + 5;\ n=1...26`

To do this, we make use of sum of n terms of an AP.

When n = 1

`2n + 5 = 2 * 1 + 5 = 7` --- T1

When n = 2

`2n + 5 = 2 * 2 + 5 = 9` --- T2

When n - 26

`2n + 5 = 2 * 26 + 5 = 57` --- T26

Next, we calculate d (common difference)

`d = T_2 - T_1`

`d = 9 - 7 = 2`

So, the sum is:

`Sum = (n)/(2)(T_1 + T_n)`

Let n = 26

So, we have:

`Sum = (26)/(2)(T_1 + T_(26))`

Substitute values for T1 and T26

`Sum = (26)/(2)(7+57)`

`Sum = (26)/(2)(64)`

`Sum = 13*64`

`Sum = 832`