Question

without adding ,find the sum 1+3+5+7+.....23

Answer 1

Hi friend
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Your answer
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1 + 3 + 5 + 7 + .....23

We can see that, this is inn AP (Arithmetic Progression).

First term (a) = 1

Common difference (d) = 3 - 1 = 2

Last term (l) = nth term (an) = 23

So,

$a_n = a + (n - 1)d$


23 = 1 + (n - 1)2

=> 2n - 2 = 23 - 1

=> 2n = 22 + 2

=> n = 24/2

=> n = 12

So, there are 11 terms in the AP.

Then,

Sum = Sn = n/2 × (a + l)

=> S12 = 12/2 × (1 + 23)

=> S12 = 6 × 24

=> S12 = 144

HOPE IT HELPS