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

Question

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

Smart Achievers · Accepted Answer

(29.5)

$Let a, a + d, a + 2 d be first three terms of an A.P.$

$So, a + a + d + a + 2 d = 39 \Rightarrow d = 3$ $(∵ a = 10)$

$Sum of last four terms = 178$

$\Rightarrow l - 3 d + l - 2 d + l - d + l = 178 \Rightarrow l = 49$

$A.P. is 10, 13, 16, 19, \dots, 46, 49 .$

$Median = \frac{10 + 49}{2} = 29.5$

Solution

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

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Solution

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

Ans. (29.5) Let a, a+d, a+2d be first three terms of an A.P. So, a+a+d+a+2d=39⇒d=3 (∵ a=10) Sum of last four terms=178 ⇒ l-3d+l-2d+l-d+l=178⇒l=49 A.P. is 10, 13, 16, 19, …, 46, 49. Median=10+492=29.5

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