Question

Express 169 as the sum of succesive odd number
starting from 1
​

Answer 1

Answer:

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 +23 + 25

Answer 2

1 + 3 + 5 + 7 + ......... + 25 = 169

Step-by-step explanation:

We can solve this in many ways, but I believe that you will understand my favourite method better

It is by Arithemetic Progression

Let's say the first term is 1 and their common difference is 2

so, a = 1 and d = 2

Thus, the A.P will be

1, 3, 5, 7, 9,........

But there is a problem we dont know the last term but we know that these numbers sum should be 169

Sn = 169

also,S(nth) = n/2[2a + (n - 1)d]

where n is the last term

Putting in the values we know, we get

169 = (n/2)[2(1) + (n - 1)(2)]

169 = (n/2)[2 + 2n - 2]

169 = (n/2)[2n]

169 = n × n = n²

Thus,

n = 13

(Remember we can't take -13 because amount of a certain value can't be negative)

For example, I can't say I have -12 sheeps but I can only say I have 0 sheep or 12 sheeps

So, we know the number of terms so we can find the last term using the formula,

a(nth) = a + (n - 1)d

a(13th) = 1 + (13 - 1)(2)

= 1 + (12 × 2)

= 1 + 24 = 25

so, the last term is 25

So, the odd successive numbers adding to 169 is

1 + 3 + 5 + 7 + ......... + 25 = 169

You can also check this in a calculator if you are not sure, this is pure maths and has to be true

Hope it helped and you understood it........All the best