Question

how many consecutive odd numbers starting from one will be added to make 100?
a.9 b.6 c.10 d.11
explain step by step .​

Answer 1

Answer:

The other answers assume that the first odd number used must be 1. But that is not specified in the question. 49 and 51 are consecutive odd numbers, and their sum is 100. So you can get a sum of 100 from 2 consecutive odd numbers.

Step-by-step explanation:

So we can do the following: Sum of odd consecutive integers from 1 to 100 = (Sum of all consecutive integers from 1 to 100) - (Sum of even consecutive integers from 1 to 100). Sum of odds = (100 x 101/2) - [2 x (50 x 51/2)] = 5050 - 2550 = 2500.

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

The number of consecutive odd numbers starting from one will be added to make 100

a. 9

b. 6

c. 10

d. 11

EVALUATION

We have to find the number of consecutive odd numbers starting from one will be added to make 100

First odd number = 1

Second odd number = 3

This is an arithmetic progression

First term = a = 1

Common Difference = d = 3 - 1 = 2

Let number of terms = n

$\displaystyle \sf{ \frac{n}{2} \bigg[2a + (n - 1)d \bigg] = 100 }$

$\displaystyle \sf{ \implies \: \frac{n}{2} \bigg[2 +2 (n - 1) \bigg] = 100 }$

$\displaystyle \sf{ \implies \: \frac{n}{2} \bigg[2 +2n - 2 \bigg] = 100 }$

$\displaystyle \sf{ \implies \: \frac{n}{2} \times 2n = 100 }$

$\displaystyle \sf{ \implies \: {n}^{2} = 100 }$

$\displaystyle \sf{ \implies \: n = 10 }$

So number of terms = 10

FINAL ANSWER

Hence the correct option is c. 10

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