Question

Solve the equation (-4) + (-1) + 2 +.........+x=437 (ARITHMETIC PROGRESSION)

Answer 1

Answer:

n= 19 an x = 50

Step-by-step explanation:

Sn = 437

An = x

A = -4

D = -1-(-4)= -1 +4= 3

now, An = A + (n-1)D

x = -4 + ( n-1)3

x = -4 + 3n - 3

x = 3n - 7      .......(1)

and Sn = n/2 ( A+ An)

Sn= n/2 ( -4 + x)

437= n/2 ( -4 + 3n - 7 )                       { by equation (1)}

 437*2= n ( 3n-11)

874 = 3n^2 - 11n

3n^2 - 11n - 874 = 0

b^2-4ac

(-11)^2- 4*3*(-874)

121+10488

10609

now n= -b±√b^2-4ac/2a

n = -(-11)±√10609/2*3

n= 11 ±103/6

when +; n= 11+103/6

n= 114/6 ⇒ 19

and when -  ; n= 11- 103/6

n= -92/6 not divisible by 6 and it is negative so this is not acceptable

hence in equation (1), n=19

so x= 3*19 -7

x= 57- 7

x= 50

Answer 2

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