Question

How many term of the AP 25, 28, 31, 34, .... are needed to give the sum 1070 ?

Answer 1

Answer:

n=20

Step-by-step explanation:

so n=20 is the answer as explained in the photo

Answer 2

HERE IS UR ANSWER : ---------

The given AP is 25,28,31,34........

here a=25 ; d= 28-25=3

sum of its first n terms = 1070

Sn=1070

n (2a+(n-1)d)= 1070

2

n(2 X 25 +(n-1)3) =1070 X 2

n(50+3n-3) = 2140

n(47+3n) = 2140

3n.n+47n-2140=0

Now this is an quadratic equation in n solving by quadratic formula we have

Discriminant D= b.b-4ac

D= 47 X 47- 4(3)(-2140)

D= 2209+25680

D= 27889

using the formula of quadratic formula we have

n= -b + root D.

2a

n = -47+167/6.

n= 120/6

n=20

case 2:

n= -b - root D

2a

n= -47-167/6

n= -214/6

n= -35.66

n cannot be negative and in fraction.

so there are 20 terms of the AP needed to give the sum of 1070.

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