the 5th and 15th term of an AP are 13 and 17 respectively. find the sum of the first 21 terms of the AP
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In the AP, 5th term = a + 4d = 13, or
a = 13 – 4d …(1)
The 15th term = a + 14d = - 17, or
a = - 17 - 14d …(2)
Equate (1) and (2)
13 – 4d = - 17 -14d, or
d= -3
a= 25
sum of first 21 terms
S = [21/2] [ 2 * 25 + (21-1) (-3)]
S = [21/2] [50 + 20 * (-3) ]
S = [21/2] [ 50 -60]
S = [21/2] [-10]
S = - 210/2
S = - 105
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