Aspire Faculty ID #9447 · Topic: NIMCET 2020 · Just now
NIMCET 2020

An arithmetic progression has 3 as its first term. Also, the sum of the first 8 terms is twice the sum of the first 5 terms. Then what is the common difference?

Solution

Step 1: Write sum formula
$S_n = \dfrac{n}{2}[2a + (n-1)d]$

$S_8 = \dfrac{8}{2}[6 + 7d] $
$= 4(6+7d) $
$= 24 + 28d$

$S_5 = \dfrac{5}{2}[6 + 4d] $
$= \dfrac{5}{2}(6+4d) $
$= 15 + 10d$

Step 2: Apply condition $S_8 = 2S_5$
$24 + 28d = 2(15 + 10d)$
$24 + 28d = 30 + 20d$
$8d = 6$
$d = \dfrac{3}{4}$

Answer: $d = \boxed{\dfrac{3}{4}}$


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Dushyant Kumar
Dushyant Kumar , Student
Commented Jun 15, 2021
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