Question

Find the sum of first 25 terms of the Ap whose 2nd term is 9and 4th term is 21

Answer 1

S25=?
a+d=9
a=d-9
a+3d=21
d-9+3d =21
4d=21+9
d=30/4=15/2
a=15/2-9=15-18/2=-3/2
S25=25/2 [2 (-3/2)+(25-1)15/2]
=25/2 [-3+24 (15/2)]
=25/2 [-3+12×15]
=25/2 [-3+180]
=25/2(177)
=4425/2
=2212.5
it is your answer

Answer 2

Answer:

S25 = 1875

Step-by-step explanation:

S25 = ?

a2 = 9  => a + d = 9 ................[i]

a4 = 21 => a + 3d = 21 .................[ii]

By subtracting [ii] from [i] we get

2d = 12

d = 6

substitue d = 6 in equation [i]

a + 6 = 9

a = 3

Sn = n/2 {2a+[n-1]d}

S25  = 25/2{2*3+[25-1]6}

s25 = 25/2{6+[24] [6]}

S25 = 25/2[6+144]

S25 = 25/2 [150]

S25 = 25*75

S25 = 1875