Question

what is the sum of first 10 natural no. in an AP​

Answer 1

Given,

a ( first term ) = 1

l ( last term ) = 10

n = 10

Formulae -

Sn ( sum of all ) = n/2 ( a + l )

Proof -

$= \frac{10}{2} (1 + 10) \\ = 5(11) \\ = 55$

Conclusion -

Sum of first 10 natural numbers = 55

Verification -

$1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 \\ = 3 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 \\ = 6 + 4 + 5 + 6 + 7 + 8 + 9 + 10 \\ = 10 + 5 + 6 + 7 + 8 + 9 + 10 \\ = 15 + 6 + 7 + 8 + 9 + 10 \\ = 21 + 7 + 8 + 9 + 10 \\ = 28 + 8 + 9 + 10 \\ = 36 + 9 + 10 \\ = 45 + 10 \\55$

// Hence proved //