The sum of the first 9 terms of an ap is 81 and that of its first 20 terms is 400 find a and D
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s9 = 81
s20 = 400
s20 = s9 + s11
400 = 81 + s11
319 = s11
319 = 11/2 {2a + (11-1)d}
319×2 = 11 {2a + 10d}
638 = 22a + 110d
58 = 2a + 10d
29 = a + 5d .... (I)
s9 = 9/2 {2a + (9-1)d}
81 = 9/2 {2a + 8d}
81×2 = 9 {2a + 8d}
162 = 18a + 72d
9 = a + 4d ... (ii)
by I and ii
29 = a+ 5d
9 = a+ 4d
-----------------
20 = d
a + 4d = 9
a + 4(20) = 9
a = 9 - 80
a = -71
s20 = 400
s20 = s9 + s11
400 = 81 + s11
319 = s11
319 = 11/2 {2a + (11-1)d}
319×2 = 11 {2a + 10d}
638 = 22a + 110d
58 = 2a + 10d
29 = a + 5d .... (I)
s9 = 9/2 {2a + (9-1)d}
81 = 9/2 {2a + 8d}
81×2 = 9 {2a + 8d}
162 = 18a + 72d
9 = a + 4d ... (ii)
by I and ii
29 = a+ 5d
9 = a+ 4d
-----------------
20 = d
a + 4d = 9
a + 4(20) = 9
a = 9 - 80
a = -71
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