Question
Find the sum:
$2 + 4 + 6 ..... + 200.$
$2 + 4 + 6 ..... + 200.$
✓
Answer
$2 + 4 + 6 + ..... + 200$
$a = 2, d = 4 - 2 = 2, l = 200 = a_n$
$\therefore\ \text{S}_{\text{n}}=\frac{\text{n}}{2}(\text{a}+\text{l})\text{ and a}_\text{n}=\text{a}+(\text{n}-1)\text{d}$
$200=2+(\text{n}-1)2$
$198=(\text{n}-1)2$
$\text{n}-1=\frac{198}{2}=99$
$\text{n}=100$
$\text{S}_\text{n}=\frac{100}{2}(2+200)$
$=50\times202$
$=10100$
$a = 2, d = 4 - 2 = 2, l = 200 = a_n$
$\therefore\ \text{S}_{\text{n}}=\frac{\text{n}}{2}(\text{a}+\text{l})\text{ and a}_\text{n}=\text{a}+(\text{n}-1)\text{d}$
$200=2+(\text{n}-1)2$
$198=(\text{n}-1)2$
$\text{n}-1=\frac{198}{2}=99$
$\text{n}=100$
$\text{S}_\text{n}=\frac{100}{2}(2+200)$
$=50\times202$
$=10100$
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