Question

Value of 1 + 3 + 5 + 7 + 9 + 11 + ………107.

Answer 1

Step-by-step explanation:

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 + 27 + 29 + 31 + 33 + 35 + 37 + 39 + 41 + 43 + 45 + 47 + 49 + 51 + 53 + 55 + 57 + 59 + 61 + 63 + 65 + 67 + 69 + 71 + 73 + 75 + 77 + 79 + 81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99 + 101 + 103 + 105 + 107

Its answer is odd no.s till 107.

Answer 2

QUESTION:

Value of 1 + 3 + 5 + 7 + 9 + 11 + ………107.

ANSWER:

series is

$1 + 3 + 5 + 7 + 9 + 11......... + 107$

we check that this is in AP or not .

so we have to find common difference.

$3 - 1 = 2$

$5 - 3 = 2$

$7 - 5 = 2$

Hence, common difference is same this series is in AP.

now we use the sum formula;

Sn = n/2 × ( a+ l )

where.

a = first term

l = last term

we have to find first number of terms in this series.

$\red{t(n) = a + (n - 1)d}$

$107 = 1 + (n - 1)2 \\ 107 = 1 + 2n - 2 \\ 107 = - 1 + 2n \\ 108 = 2n \\ n = 54$

$\pink{total \: terms(n) = 54}$

now come to main question;

here

$first \: term(a) = 1$

$last \: term (l)= 107$

so,

$s(54) = \frac{54}{2} (1 + 107) \\ s(54) = 27 \times 108 \\ s(54) = 2916$

FINAL ANSWER :

$\huge\red{2916}$

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