Find the sum of the first 100 odd numbers?
Given: 100
Solution:
➜First we can Address the formula, then input the parameters and values.
[tex] \: \: \: \: \rm The \: first \: term: a_n = 1[/tex]
[tex] \: \: \: \: \rm The \: Common \: deference: d = 2[/tex]
[tex]\: \: \: \: \rm The \: Total \: number \: of \: the \: term: n = [100][/tex]
➜Then we can apply the input parameter value in the AP formula so:
[tex]\large\: \: \: \: \rm Sum = \frac{ \: \: n \: \: }{2x} (a+Tn)[/tex]
[tex]\large \: \: \: \: \rm = \frac{ \: 100 \: } {2}\tt (2a + (n - 1)d) \\ \large \rm \: \: \: \: = \frac{ \: 100 \: } {2}(2 \times 1) + (100 - 1) \\ \large \to\times 2 \\ \large \rm = \frac{ \: 100 \: } {2}(2 + 198) \\ \large \rm = 50 \times 200 \\ \large \rm = {\underline{\green{ \: 10000 \: }}}[/tex]
[tex]\large\therefore\tt So \: the \: sum \: of \: the \: first \\ \large\tt \: 100 \: odd \: numbers \: is: \\ { \underline{ \: \: \boxed{\large\rm \green{ \: 10000 \: }} \: \: }}[/tex]
[tex] \\ \\ [/tex]
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