Question

If the sum of the first two terms of an arithmetic progression is equal to the sum of the first three terms of the same arithmetic progression then find the sum of the first five terms of the same arithmetic progression.

Answer 1

ANSWER

Let the first term of AP be a and difference be d

Then third term will be =a+2d

${15}^{th} \: will \: be = a + 14d$

${6}^{th} \: will \: be = a + 5d$

$1 {1}^{th} \: will \: be = a + 10d$

$1 {3}^{th} will \: be = a + 12d$

$then \: the \: eq. \: will \: be$

$a + 2d + a + 14d = a + 5d + a + 10d + a + 12d$

$= > 2a + 16d = 3a + 27d$

$= > a + 11d = 0$

$we \: understand \: a + 11d \: will \: be \: the \: 1 {2}^{th} \: term \: of \: arithmetic \: progression.$

$so, \: CORRECT \: answer \: is \: {\boxed {\pink{12}}}$

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