Question

find the sum of the first 20 odd numbers.
solution:
answer:​

Answer 1

Answer:

1+3+5+7+9+11+13+15+17+19+21+23+25+27+29+31+33+35+37+39

=400

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Answer 2

first 20 odd numbers are in ap = 1,3,5,7..................

here,

a = 1

$d = \binom{a}{ \: \: \: 2} - \binom{a}{ \: \: \: 1}$

d = 3 - 1 = 2

d = 2

by the formula:-

$\binom{s}{ \: \: \: n} = \frac{n}{2} (2a + (n - 1)d)$

$\binom{s}{ \: \: \: 20} = \frac{20}{2} (2(1) + (20 - 1)2)$

$\binom{s}{ \: \: \: 20} = {10}( 2 + (19)2)$

$\binom{s}{ \: \: \: 20} = 10(2 + 38)$

$\binom{s}{ \: \: \: 20} = 10 \times 40$

$\binom{s}{ \: \: \: 20} = 400$

hence, the sum of first 20 odd number is 400.