In the arithmetic progression 27,24,21 sum of how many terms will be 132 and give reason. About the author Lyla
Answer: a1 = 27 , a2 = 24 a2 – a1 = d 24 – 27 = -3 Sn = n/2 [2a + (n-1)d] 132 = n/2 [2×27 + (n-1)×-3] 132 = n/2 [ 54 -3n +3] 132 = n/2 [57 – 3n] 132×2 = n[57 – 3n] 264 = 57n – 3n² 57n – 3n² – 264 = 0 -3n² + 57n – 264 = 0 Multiplying by -1 3n² – 57n + 264 = 0 Dividing by 3 n² – 19n + 88 = 0 a + b = -19 a × b = 88 -11 + -8 = -19 -11 × -8 = 88 n² – 19n + 88 = 0 n² – 11n – 8n + 88 = 0 n(n – 11) -8 (n – 11) = 0 (n – 8) (n -11) =0 n = 8 or n = 11 I hope this will help u. Please add this to the brainlist. Reply
Answer:
a1 = 27 , a2 = 24
a2 – a1 = d
24 – 27 = -3
Sn = n/2 [2a + (n-1)d]
132 = n/2 [2×27 + (n-1)×-3]
132 = n/2 [ 54 -3n +3]
132 = n/2 [57 – 3n]
132×2 = n[57 – 3n]
264 = 57n – 3n²
57n – 3n² – 264 = 0
-3n² + 57n – 264 = 0
Multiplying by -1
3n² – 57n + 264 = 0
Dividing by 3
n² – 19n + 88 = 0
a + b = -19
a × b = 88
-11 + -8 = -19
-11 × -8 = 88
n² – 19n + 88 = 0
n² – 11n – 8n + 88 = 0
n(n – 11) -8 (n – 11) = 0
(n – 8) (n -11) =0
n = 8 or n = 11
I hope this will help u. Please add this to the brainlist.