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Question

In a HP the 7th term is 17 and 14th term is 1. Find the third term .

A
10.45
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B
12.45
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C
14.65
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D
15.25
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Solution

The correct option is A 10.45
7th term of HP = 17, then the reciprocal of 7th term is AP =7.
t7=7
But we know that
tn=a+(n1)d
t7=a+6d
a+6d=7---- (1)
According to the problem, 14th term of HP is 1.
Then the reciprocal of AP is 1.
Hence, 14th term of AP is 1
t14=1
t14=a+(n1)d
a+13d=1---- (2)
Equating equation 1 and 2,
7d=6
d=67
Substitute the value of d in equation (1),
a+6(67)=7
7a+36=49
7a=4936
a=12.14
We know the general term of AP given by tn=a+(n1)d
Third term of AP, t3=12.14+(31)67
t3=12.14127
t3=10.45

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