Question

☆ONLY FOR MODERATORS OR MATHS GENIUS☆<br /><br />$find \: the \: sum \: of \: first \: 20 \: terms \: of \: \\ the \: series \\ 2 + 13 + 28 + 47 + 70.......$<br />●●●●●●●●●●●●●●●●●●●●●<br />♡SOLUTION MUST<br />♡NO SPAMMING<br />♡CONTENT QUALITY REQUIRED<br /><br />▪▪▪▪▪▪▪▪▪▪▪▪▪▪<br />ONLY BEST AND EXPLAINED ANSWERS WILL BE MARKED AS BRAINLIEST <br />▪▪▪▪▪▪▪▪▪▪▪▪▪

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ANSWER IS 6690
EXPLAIN HOW??

Answer 1

Here,


Series:-2,13,28 47

Now, there CommOn difference

2(difference)13=11


13(diffrrence)28=15

28 (difference)47=19


Again,


Second Difference

11,15,19

15-11=4


19-15=4


then,


Using ....

Quardratic Formula:-

ax²+bx+c

Let to be first term (1)


then,
value=2

a(1)²+b(1)+c

a+b+c=2(a)


When second term (2) then. value=13


Now,


ax²+bx+c=13

a(2)²+b(2)+c=13


4a+2b+c=13 (b)




Again...

when the term (3) value=28


a(3)²+b(3)+c

9a+3b+c=28(c)


Solving Equation a,b,and c

we get,


Value
a=2
b=5

c=-5


Putting the value of ax²+bx+c


Now,


2(x)²+5(x)+(-5)

2x²+5x-5




Here,


Using summation....

2(Summation(x²)+5 x-5


Now,


[ 2 x { (20 x 21 x 41)/6}] + [ 5 x ( 20x21/2)] - (5 x 20)]


(140 x 41) + (50 x 21) - 100= 6690






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