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Question
Mark the correct alternative in each of the following:
If 7th and 13th terms of an A.P. be 34 and 64 respectively, then its 18th term is
Options
87
88
89
90
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Solution
In the given problem, we are given 7th and 13th term of an A.P.
We need to find the 26th term
Here,
a7 = 34
a13 = 64
Now, we will find a7 and a13 using the formula
an = a + (n-1) d
So,
a7 = a + (7 - 1 ) d
34 = a + 6d .............(1)
Also,
`a_13 = a + (13 - 1 ) d`
64 = a + 12 d ........(2)
Further, to solve for a and d
On subtracting (1) from (2), we get
64 - 34 = (a + 12d) - (a + 6d)
30 = a + 12d - a -6d
30 = 6d
`d = 30/6`
d = 5 ................(3)
Substituting (3) in (1), we get
34 = a + 6(5)
34 = a + 30
a = 34 - 30
a = 4
Thus,
a = 4
d = 5
So, for 18th term (n = 18),
Substituting the above values in the formula, an = a + (n-1) d
a18 = 4 + (18 - 1) 5
= 4 + 17 (5)
= 4 + 85
= 89
Therefore, a18 = 89
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