a = 7 , d = -3 answer
Step-by-step explanation:
Snth= n/2[2a+(n-1)]
S9th= 9/2[2a +(9-1)d]
S9th= 9(a + 4d)
S9th = 9a + 36d
9a + 36d = 171
a + 4d = 171/9
a + 4d = 19.........................(1)
S24th = 24/2[2a + (24-1)d]
S24th = 12[2a + 23d]
12[2a + 23d] =996
2a + 23d = 83 ............(2)
multiple eq (1) by 2
2a +8d = 38 ...................(1)
from (1)& (2)
2a +23d = 83
2a_+_38d_=_38
-__-________-___
0. -_15d__=45
d = - 3
put the value of d in eq (1)
a +4d = 19
a + 4 (-3) = 19
a -12 = 19
a = 7
common difference (d) = -3
first term (a) = 7
Given,
S9=171
S24-996
Sn=n/2(2a+(n-1)d)
S9=9/2(2a+(9-1)d) 171=9/2(2a+8d)
171=9(a+4d)
a+4d=19-------(1)
Similarly,
S24-12(2a+23d)
276=12(2a+23d)
2a+23d=23---- -(2)
From equation (1) and (2), we get
d= -1 and a=23
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Verified answer
a = 7 , d = -3 answer
Step-by-step explanation:
Snth= n/2[2a+(n-1)]
S9th= 9/2[2a +(9-1)d]
S9th= 9(a + 4d)
S9th = 9a + 36d
9a + 36d = 171
a + 4d = 171/9
a + 4d = 19.........................(1)
S24th = 24/2[2a + (24-1)d]
S24th = 12[2a + 23d]
12[2a + 23d] =996
2a + 23d = 83 ............(2)
multiple eq (1) by 2
2a +8d = 38 ...................(1)
from (1)& (2)
2a +23d = 83
2a_+_38d_=_38
-__-________-___
0. -_15d__=45
d = - 3
put the value of d in eq (1)
a +4d = 19
a + 4 (-3) = 19
a -12 = 19
a = 7
common difference (d) = -3
first term (a) = 7
Given,
S9=171
S24-996
Sn=n/2(2a+(n-1)d)
S9=9/2(2a+(9-1)d) 171=9/2(2a+8d)
171=9(a+4d)
a+4d=19-------(1)
Similarly,
S24-12(2a+23d)
276=12(2a+23d)
2a+23d=23---- -(2)
From equation (1) and (2), we get
d= -1 and a=23