Let the sum of the first three terms of an A.P. be 39 and the sum ofn its last four terms be 178 . If the first term of this A.P. is 10 ,n then the median of the A.P. is

(c) : Let a, a+d, a+2 d be first three terms of an A.P.n nSo, a+a+d+a+2 d=39nSum of last four terms =178nn n => l-3 d+l-2 d+l-d+l=178 n => 4 l-6 d=178 => 4 l=196 => l=49n nnA.P. is 10,13,16,19,46,49nn Median =(10+49 / 2)=29.5n

Let the sum of the first three terms of an A.P. be 39 ... | Sequence & Series (Mathematics)

a, a+d, a+2 d

be first three terms of an A.P.\n \nSo,

a+a+d+a+2 d=39

\nSum of last four terms

=178

\n\begin{aligned}\n& \Rightarrow l-3 d+l-2 d+l-d+l=178 \\\n& \Rightarrow 4 l-6 d=178 \Rightarrow 4 l=196 \Rightarrow l=49\n\end{aligned}\n

\nA.P. is

10,13,16,19,46,49

\n\text { Median }=\frac{10+49}{2}=29.5\n

Explanation

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