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Question
The 10th and 18th terms of an A.P. are 41 and 73 respectively. Find 26th term.
Solution
In the given problem, we are given 10th and 18th term of an A.P.
We need to find the 26th term
Here
`a_10 = 41`
`a_18 = 73`
Now we will find `a_10` and `a_18` using the formula `a_n = a + (n -1)d`
So,
`a_10 = a + (10 - 1)d`
41 = a + 9d ....(1)
Also
`a_18 = a + (10 - 1)d`
73 = a + 17d .....(2)
So to solve for a and d
On subtracting (1) from (2) we get
8d = 32
`d - 32/8`
d = 4
Substiting d= 4 in (1) we get
41 = a + 9(4)
41 - 36 = a
a = 5
Thus
a = 5
d = 4
n = 26
Substiting the above values in the formula `a_n = a + (n -1)d`
`a_26 = 5 + (26 - 1)4`
`a_26 = 5 + 100`
`a_26 = 105`
Therefore `a_26 = 105`
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