Question

How many terms of the AP 25,28,31,34....Are needed to give the sum 1070.

Answer 1

a=25
d=a2-a1
d =28-25
d=3
sn =1070
by using the formula sn=n/2(2a+(n-1)d)


1070=n/2(50+(n-1)(3))
2140=n(50+3n-3)
2140=n(47+3n)
2140=47n+3n square

now solve this equation by the quadratic formula or middle term splitting.

Answer 2

ANSWER :

Sn = 1070
a = 25
d = 28 - 25 = 3
n = ?

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

1070 = n/2 [ 2 x 25 + ( n - 1 ) 3 ]

1070 x 2 = n [ 50 + 3n - 3 ]

2140 = n ( 47 + 3n)

2140 = 47n + 3n sq.

3n sq. + 47n - 2140 = 0

3n sq. + 60n - 107n - 2140 = 0

3n ( n + 20) - 107 ( n + 20) = 0

( 3n - 107) (n + 20) = 0

3n = 107
n = 107 /3
n = 35.6


n = -20

terms required = 36


hope it helps