Write 5^ th term from the end of the A.P. 3, 5, 7, 9, ....., 201 - Vidyadip

Question

Write $5^{th}$ term from the end of the $A.P. 3, 5, 7, 9, ....., 201$

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Answer

Given,
$A.P, 3, 5, 7, 9, ..... 201$
Here, First term a = 3
Difference d = 5 - 3 = 2
and Last term $a_n = 201$
We knaw,
$a_n = a + (n - 1)d$
$\Rightarrow 201 = 3 + (n - 1)2$
$\Rightarrow 201 = 3 + 2n - 2$
$\Rightarrow 201 = 1 + 2n$
$\Rightarrow 2n = 201 - 1$
$\Rightarrow 2n = 200$
$\Rightarrow\ \text{n}=\frac{100}{2}$
$\Rightarrow n = 100$
Now, we have to find $5^{th}$ term from the end $100^{th} - 4^{th} = 96^{th}$
$a_n = a + (n - 1)d$
$\Rightarrow a_{96} = 3 + (96 - 1)2$
$\Rightarrow a_{96} = 3 + 95 \times 2$
$\Rightarrow a_{96} = 3 + 190$
$\Rightarrow a_{96} = 193$
Hence, $5^{th}$ term from the end of given A.P. is 193.

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