☆ONLY FOR MODERATORS OR MATHS GENIUS☆<br /><br />[tex]find \: the \: sum \: of \: first \: 20 \: terms \: of \: \\ the \: series \\ 2 + 13 + 28 + 47 + 70.......[/tex]<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??
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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