What would be sum of 10th row of the below given series

1

2 3

4 5 6

7 8 9 10

11 12 13 14 15

………………………………..

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This is a pyramid of numbers in which every row includes that much numbers as the rows place. …So either start from 1,2,4,7….find the first no. Of tenth row and add those ten no or Start from from 1,3,6,10….find the last no….then reduce to ten no. Before that no ….Nd add it ….therefore ll be 101×5=505

505 is the ans.

I calculated the ans. As follows

I saw that the series is in A.P so calculated the total sum and used the basic sum formula of AP.

(46,47,…55)

505…. It's based on the AP… If we notice the left side it is a series and we can obtain Ap by subtracting the same no. Just increase there place value by 1 i.e 2-1,4-2,7-4….=1,2,3….

So 1+(1+2+3+…..9)=46(our first no. Of 10th row

We have our 10th row 46,47,48…….55 =10*(46+55)/2=505

{N (n+ 1)}/2. Use 2 time. & ——-

505

505

505

505

series is 46 to 55

ans =(55*28)-(45*23)=505

505 ans

505

505

505,from 46 to 55

Sir this question solved as 46 to 55 no tak sum so S=n(a+l)/2 …. n is total no is 10 and a is starting no 46 . l is last no 55 then S=10(46+55)/2=505 ans

505

Since the fifth row will be start from 45to 55.applying the sum formula of AP I. e n/2(a+l) we get 505 as the ans

505

505

505 is Answer

1 row 1 number

2 row 2 number

9 row 9 number total 45 numbers are used so 10th row start by 46 to 55

So sum is 505

505

because in 6 th serease six no added AND seventh serease 7 nobers added and so on similarly in 10th serease 10 no added that is 46 to 55 and use ap n/2{a+l}=505 ans

For 2nd last term is 3

(2*3/2)==3

For third row last term is 6

(3*4/2)==6

Fourth row last term is 10

(4*5/2)==10

Similarly last term of 9th row will be (9*10/2)==45

First term is 46 and this row has 10 terms

(n/2)(a+(n-1)*1)==(a=46,n=10)

505

505

इफ्तिखार चौधरी जैसलमेर

505

We can work on the middle term…1 in 1st row, 5 in 3rd row, 13 in 5th row ,25 in 7th row and 41 in the 9th row..or we have (41+9)=50 and (41+10)=51 as the 2 middle term in the 10th row..so (50+51)/2=50.5*10=505 is the ans