Question

find the number of terms in following series if 15+12+9+6+..............................=-90​

Answer 1

hi there mate!!!

Solution:

here,

a= first term= 15

common difference= -3.

now,

according to the formula for finding the sum,

Sn= n/2[ 2a+(n-1)×d]

-90= n/2[30+(-3n+3)]

-90=n/2[33-3n]

-90=33n-3n^2/2

now,

-90×2= 33n-3n^2

-180=33n-3n^2

hence,

3n^2-33n-180=0

n^2-11n-60= 0.......required quadratic polynomial.

now,

by factorization method,

n^2-15n+4n-60= 0

n(n-15) +4(n-15) =0

(n-15) (n+4) =0

n= 15 or n= -4

but we know,

number of terms cannot be negative and hence, n= -4 is discarded.

hence,

n= 15

Therefore, the number of terms in the series is 15

hope this helps!! ☺❤✌

Answer 2

-4 is neglected because ,the term no will never be negative

so, the answer is 15 term