Answer:
[tex]Sum = 832[/tex]
Step-by-step explanation:
Given
See attachment
Required
Evaluate
The expression can be expressed as:
[tex]Sum = 2n + 5;\ n=1...26[/tex]
To do this, we make use of sum of n terms of an AP.
When n = 1
[tex]2n + 5 = 2 * 1 + 5 = 7[/tex] --- T1
When n = 2
[tex]2n + 5 = 2 * 2 + 5 = 9[/tex] --- T2
When n - 26
[tex]2n + 5 = 2 * 26 + 5 = 57[/tex] --- T26
Next, we calculate d (common difference)
[tex]d = T_2 - T_1[/tex]
[tex]d = 9 - 7 = 2[/tex]
So, the sum is:
[tex]Sum = \frac{n}{2}(T_1 + T_n)[/tex]
Let n = 26
So, we have:
[tex]Sum = \frac{26}{2}(T_1 + T_{26})[/tex]
Substitute values for T1 and T26
[tex]Sum = \frac{26}{2}(7+57)[/tex]
[tex]Sum = \frac{26}{2}(64)[/tex]
[tex]Sum = 13*64[/tex]
[tex]Sum = 832[/tex]
