Question

The avg of 25 consecutive odd no. Is 49
Find smallest no.

Answer 1

Let the smallest number of the 25 consecutive odd numbers be denoted by the variable a.

$Average = \frac{Sum}{Number \: of \: terms}$

$Sum \: of \: 25 \: terms: \\ = \frac{n}{2} (2a + (n - 1)d)$

Where n = 25, I.e. the number of terms, a is the smallest number and d is the common difference between the consecutive odd numbers I.e. 2.

Substituting the values in the formula :

$= \frac{25}{2} (2 a + (25 - 1)2) \\ \\ = \frac{25}{2} (2a + 24 \times 2) \\ \\ = \frac{25}{2} (2a + 48) \\ \\ = 25(a + 24) \\ \\ = 25a + 600$

$49 = \frac{25a + 600}{25} \\ \\ 49 = a + 24 \\ \\ a = 25$

Therefore, the smallest number is 25.

Answer 2

Answer:-

Smallest number is 25

$((2a + (n - 1)d) )$

25terms

$((2 a + (25 - 1)2))$

$((2a + 24 (2a + 48) )$

$(= 25(a + 24)$

$(25a 65(225)$

2a+(25−1)2)

$</p><p>(2a+24×2) (2a+48)</p><p>$

$(25a + 600)$

$(49=a+24)</p><p> \\( a=25)$