If the sum of first 9 terms of an A.P is 36 and its
7th term is 2, then the sum of its first 17 terms is:
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Step-by-step explanation:
S9 = 36
t7 = 2
S17 = ?
Sn = n/2 [ 2a + (n - 1) d]
S9 = 9/2 [ 2a + (9 - 1) d]
36 = 9/2 ( 2a + 8d)
36 = 9/2 × 2( a + 4d)
36 = 9 ( a + 4d)
36/9 = a + 4d
•°• a + 4d = 4 ______(1)
tn = a + (n - 1) d
t7 = a + ( 7 - 1) d
2 = a + 6d
a + 6d = 2______(2)
Subtracting equation (2) from (1)
a + 4d = 4
—
a + 6d = 2
____________
- 2d = 2
d = 2/-2
d = -1
Substituting value of d in equation (1)
a + 4d = 4
a + 4(-1) = 4
a - 4 = 4
a = 4 + 4
a = 8
Sn = n/2 [ 2a + (n - 1) d]
S17 = 17/2 [ 2(8) + (17 - 1)(-1)]
S17 = 17/2 [ 16 + (-16)]
S17 = 17/2 ( 16 - 16)
S17 = 17/2
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