Math, asked by legendarysumit, 1 year ago

Hiii, brainy users

A tricky question

without adding find the sum

1)1+3+5+7

2)1+3+5+7+9+11

3)1+3+5+7+9+11+13+15+17+19+21

CONTENT QUALITY ANSWER NEEDED

no spam answers from answers will be deleted on the spot


SamriddhaChandra: 7×7 = 14
BrainlyPrincess: it must be 7 +7 and not 7 * 7
SamriddhaChandra: my bro is doing these things sorry from him
SamriddhaChandra: I'm telling u the and
SamriddhaChandra: 4×4 = 16
SamriddhaChandra: 6 × 6 = 36
SamriddhaChandra: 11 × 11= 121
SamriddhaChandra: these r the 3 answers. it is said that n×n = first n odd natural numbers. so in this way the 3 answers will be 16, 36 and 121 respectively
SamriddhaChandra: legendary sumit, is my ans right??
legendarysumit: yes I am answering your questions and mark my brain l i e s t I needed to the next

Answers

Answered by siddhartharao77
6
Let a be the first term and d be the common difference.

(1).

Here 1st term a = 1.

last term l = 9.

Number of terms n = 4.

We know that sum of n terms sn = n/2(a + 7)

                                                       = 4/2(1 + 7)

                                                       = 4/2(8)

                                                       = 4 * 4

                                                       = 16.




(2) Here a = 1, l = 11, n = 6.

We know that sum of n terms sn = n/2(a + l)
 
                                                        = 6/2(1 + 11)

                                                        = 6/2(12)

                                                         = 6(6)

                                                         = 36.



Therefore the sum = 36.




(3) 

Method (1):

We know that sum of 1st n odd number = n^2

here total number of terms = 11.

Therefore the sum = (11)^2

                                 = 121.



Method (2):

a = 1, n = 11, d = 2.

We know that nth term of an AP an = n/2 [2a + (n - 1) * d]

                                                            = 11/2[2(1) + (11 - 1) * 2]

                                                            = 11/2[2 + 10 * 2]

                                                             = 11/2[2 + 20]

                                                              = 11/2[22]

                                                              = 11 * 11

                                                              = 121.



Hope this helps!

siddhartharao77: :-)
legendarysumit: good man
siddhartharao77: Then y u reported my answer
legendarysumit: because you're not wrote it in a perfect Manner
siddhartharao77: Ohkkk...Thanks
legendarysumit: okay brother ur class
siddhartharao77: When you dont like the answer, tell directly..No need to report...
siddhartharao77: Bye
legendarysumit: okay
Answered by SamriddhaChandra
2

we know that, for any natural number n,
n×n = sum of first n natural numbers.
this is a special property of rational numbers

Keeping this property in mind, we have

1) 1+3+5+7 = sum of first 4 natural numbers = 4×4 = 16

2) 1+3+5+7+9+11 = sum of first 6 natural numbers = 6×6 = 36

3) 1+ 3 +5+7+9+11 +13+15+17+19+21 = sum of first 11 natural numbers= 11 × 11 = 121


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