The sum of first seven terms of an A.P. is 182. If its 4th and the 17th terms are in the ratio 1 : 5, find the A.P.
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Answered by
15
Answer:
The AP is 2,10,18,26,.......
Step-by-step explanation:
Given :
S7 = 182 , a4 : a17 = 1 : 5
Now,
a4 / a17 = 1/5
By using the formula ,an = a + (n - 1)d
a + (4 -1)d/a + (17 - 1)d = 1/5
(a + 3d)/(a + 16d) = ⅕
5(a + 3d) = 1(a + 16d)
[By cross multiplication]
5a + 15d = a + 16d
5a - a = 16d - 15d
4a = d
d = 4a ………….. (1)
By using the formula ,Sum of nth terms , Sn = n/2 [2a + (n – 1) d]
S7 = 7/2[2a + (7 - 1)d)]
182 = 7/2 [2a + 6d]
182 = 7/2 × 2[a + 3d]
182/7 = a + 3d
a + 3d = 26
a + 3(4a) = 26
[from eq (1)]
a + 12a = 26
13a = 26
a = 26/13
a = 2
First term ,a = 2
On putting the value of a = 2 in eq 1,
d = 4a
d = 4 × 2
d = 8
Common Difference,d = 8
The required AP is a , a+d , a + 2d , a,+ 3d , a + 4d ……
Hence, the AP is 2,10,18,26,.......
HOPE THIS ANSWER WILL HELP YOU…..
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