Question

Find the ${31}^{st}$ term of an A.P. whose ${11}^{th}$ term is 38 and the ${16}^{th}$ term is 73.
[2 marks]
[NCERT]
[nth Term of an AP]

Answer 1

Solution:
Given that, $a_{11}=38$ and $a_{16}=73$
We know that, $a_n=a+(n-1)d$
$a_{11}=a+(11-1)d$
$38==a+10d$ ...(1)
Similarly, $a_{16}=a+(16-1)d$
$73=a+15d$ ...(2)
On subtracting (1) from (2), we obtain
35 = 5d
d = 7
[1 mark]

From equation (1),
$38=a+10\times \left(7\right)$
38 - 70 = a
a = -32
$a_{31}=a+(31-1)d$
$=-32+30\left(7\right)$
$=-32+210$
=178
Hence, ${31}^{st}$ term is 178.
[1 mark]
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