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Find the five terms of an AP whose sum is 12 and first and last term ratio
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3
Answers
Answered by
3
Answer:
Sum of an AP is give by
S
n
=
2
n
[2a+(n−1)d]
Since sum of first 5 terms is given so
S
5
=
2
5
[2a+(5−1)d]
2
25
=
2
5
[2a+4d]
a+2d=
2
5
..(1)
Also given,
d
a
=
3
2
a=
3
2d
......(2)
Putting value of a from (2) to (1) we get
3
2d
+2d=
2
5
3
2d+6d
=
2
5
4d+12d=15
16d=15
d=
16
15
Putting value of d in (2)
a=
3
2d
=
3
2
×
16
15
=
8
5
Therefore, first five terms of an AP are a,a+d,a+2d,a+3d,a+4d
i.e.
8
5
,
16
25
,
16
40
,
16
55
,
16
70
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