1. If the 5th term of an AP is 19 and the sum of the first 5th term is 65, then A.P. is?
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Answer:
A.P is 7, 10, 13, 16, 19... so on.
Step-by-step explanation:
Given we have An = 19 and Sn = 65 and n = 5
An = a + (n-1)d
19 = a + ( 5-1 ) d
19 = a + 4d - (1)
Sn = n/2 ( 2a + (n-1) d)
65 = 5/2 ( 2a + (5-1) d)
65 = 5/2 ( 2a + 4d)
65 * 2/5 = 2 (a + 2d)
26 / 2 = a + 2d
13 = a + 2d - (2)
By elimination method in equation 1 and 2,
(a-a) + (4d - 2d) = 19 - 13
2d = 6
d = 6/2
d = 3
a + 2d = 13
a + 2(3) = 13
a+ 6 = 13
a = 13 - 6
a = 7
so, A.P :- a, a+d, a+2d, a+3d, a+4d
= 7, 10, 13, 16, 19... so on.
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