Find the $31$ st term of an AP whose $11$ th term is $38$ and $16$ th term is $73$ .

150

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165

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168

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178

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Solution

The correct option is B $178$
$a + 10 d = 38$ .......(i)
and $a + 15 d = 73$ ..........(ii)
Solving eq. (i) and (ii) we get
$5 d = 35 \Rightarrow d = 7$
$a = - 32$
$∴ a_{31} = a + 30 d = - 32 + 30 (7)$
$= - 32 + 210 = 178$

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State whether True or False. The $31^{s t}$ term of an AP whose $11^{t h}$ term is 38 and $16^{t h}$ term is 73 is 178.

Find the 31^st term of an A.P. whose 11^th term is 38 and the 16^th term is 73

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