Question

how many terms of the A.P. 93+90+87+84 will amount too 975 ?

Answer 1

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Topic:- Arithmetic Sequence or Progression

Tn=a+(n-1)d

Sn=n/2(2a+(n-1)d)

We have;

Sn=975

a=93

d=90-93=-3

d=-3

==========≠===============

Substitute the value of Required terms!

Sn=n/2(2a+(n-1)d

975=n/2(2×93+(n-1)-3

975=n/2(186-3n+3)

975=n/2(189-3n)

975×2=n(189-3n)

1950=189n-3n²

1950-189+3n²

3n²-189+1950

3(n²-63+650)=0

n²-63n+650

n²-50n-13n+650

n(n-50)-13(n-50)

(n-50)(n-13)

n=13


===========n}=13=====

Answer 2

Given first term = 93
common difference = -3
then let nos. be n
then 975 = n/2(2*93+(n-1)-3)
975 = n/2(186-3n+3)
975 = n/2(189-3n)
1950 = 189n -3n^2
Dividing by 3
we get 650 = 63n - n^2
so n^2 -63n +650 = 0
n^2 -50n-13n +650 = 0
n(n-50) -13(n-50) = 0
(n-13)(n-50) = 0
So 13 terms would add up to 975.