Question

Find the sum A. P
$1 + 3 + 5 + .... + 199$
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Answer 1

Answer:

I think your answer is 10000

Answer 2

Given ,

• First term (a) = 1
• Common difference (d) = 2
• nth term (an) = 199

We know that , the nth term of an AP is given by

$\boxed{ \sf{ a_{n} = a + (n - 1)d }}$

Thus ,

199 = 1 + (n - 1)2

198 = (n - 1)2

n - 1 = 99

n = 100

Now , the sum of first n terms of an AP is given by

$\boxed{ \sf{S_{n} = \frac{n}{2} (a + a_{n})}}$

Thus ,

Sn = 100/2 × (1 + 199)

Sn = 50 × 200

Sn = 1000

Therefore ,

• The sum of AP is 1000