Question

The sum of 5 numbers in ap is 30 and the sum of their squares is 220. which of the following is the third term?​

Answer 1

Answer:

answer can be easily found in this way-

5 terms of an A.P can be represented in the form as a-2d,a-d,a,a+d,a+2d.

then sum = a-2d + a-d + a + a+2d +a+d that is 30

so after addind a = 6.

that is answer

Answer 2

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$let \: 5 \: numbers \: in \: ap \: be \: (a - 2d) + ( a - d) + a + (a + d) + (a + 2d) \\ given \: that \: : (a - 2d) + ( a - d) + a + (a + d) + (a + 2d) = 3 0 \\ 5a = 30 \\ \therefore \: a = 6 \\ sum \: of \: their \: squares \: is \: 220 \\ : (6 - 2d) {}^{2} + ( 6- d) {}^{2} + 6 {}^{2} + (6 + d) {}^{2} + (6 + 2d) ^{2} = 220 \\ 4d { }^{2} + d {}^{2} + d {}^{2} + 4d {}^{2} + 36 +3 6 + 36 + 36 + 36 = 220 \\ 10d {}^{2} =220 - 180 \\ d { }^{2} = \frac{40}{10 } \\ d = \sqrt{4 } \\ d = 2 \\ now \: third \: term \: of \: ap = a + (3 - 1)d \\ a {}^{3} = 6 + 2 \times 2 \\ third \: term \: of \: ap \: is \: 10$