The sum of the first 7 terms of an AP is 182. If its 4 th and 17 th terms are in the ratio 1:5
find the AP
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Given,
S
7
=
2
7
[2a+(7−1)d]=182
182=
2
7
[2a+6d]........(1)
a
n
=a+(n−1)d
a
4
=a+(4−1)d=a+3d
a
17
=a+(17−1)d=a+16d
From given, we have,
a
17
a
4
=
a+16d
a+3d
5
1
=
a+16d
a+3d
5a+15d=a+16d
solving the above equation, we get,
4a=d
using this value in (1), we get,
182=
2
7
[2a+6(4a)]
solving the above equation, we get,
a=2
4(2)=8=d
The series as follows,
a,a+d,a+2d,.........
⇒2,10,18,.......
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