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Arithmetic Progression — Maths STD 10 — Question

Gujarat BoardEnglish MediumSTD 10MathsArithmetic Progression4 Marks
Question
Find four numbers in $AP$ whose sum is $28$ and the sum of whose squares is $216.$
✓

Answer

  1. Their sum
$(a - 3d) + (a - d) + (a + d) + (a + 3d) = 28$
$4a = 28$
$a = 7.$
  1. Their product
$ (a-3 d)^2+(a-d)^2+(a+d)^2+(a+3 d)^2=216$
$ 4 a^2+20 d^2=216 $
$ a^2+5 d^2=54$
$\text { Putting the value of a }$
$ 49+5 d^2=54 $
$ 5 d^2=5 $
$d^2=1$
$\text{d}=\pm1.$
Hence, the numbers are $4, 6, 8 \& 10.$

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