Question

(-4) + ( -1) +2 + 5 +.........+ x = 45 ​

Answer 1

Given➛(RIGHT QUESTION)

Series ➠

(-4) + ( -1) +2 + 5 +.........+ x = 35

______________________________

TO FIND➛

Number of Terms in Series?

______________________________

SOLUTION➛

Given Series will be in A.P

if Difference between two consecutive terms remain always same.

if

-1-(-4) =2-(-1) =5-3

then, Series is in A.p

3 = 3 = 3

which is true,

Hence,given series is in A.P.

Let us know What is A.p?

Series will be called in A.p, if the difference between two consecutive terms is remain same for all terms.

____________________________

Now,

ATQ➽

(-4) + ( -1) +2 + 5 +.........+ x = 35

is in A.p

where,

a= -4

d= 3

sum of N terms is = 35

then,

Sum of terms = n/2×(2a+(n-1)d)

35 = n/2 × (2(-4)+(n-1)3)

70=n(-8+3n-3)

70 = -11n+3n^2

70+11n-3n^2=0

Now,

This equation is in Quadratic,

Let solve this quadratic equation:-

70-10n+21n-3n^2=0

10(7-n)+3n(7-n)=0

(10+3n)(7-n)=0

therefore,

n=7 or -10/3

But terms will never be in Negative terms or in Fraction,

Therefore.

n=7✔️

______________________________

ANSWER➠

Number of Terms in this A.p sum=>

7

Answer 2

Answer:

7 is the missing number ..........