Question

An arithmetic progression s1=5 s2=12 then value of 'd' is

Answer 1

$\bf Given:\ \sf S_1\ =\ 5\ and\ S_2\ =\ 12.\\\\\bf To\ find:\ \sf The\ common\ difference\ [d].\\\\\bf Answer:\\\\\sf We\ know\ that\ S_1\ =\ a_1,\ the\ first\ term. \\\\Hence,\ the\ first\ term\ of\ the\ A.P.\ is\ \bf 5.\\\\\\\sf S_2\ -\ S_1\ =\ a_2\\\\12\ -\ 5\ =\ 7\\\\The\ second\ term\ is\ \bf 7.\\\\\sf Therefore,\ the\ A.P.\ is\ 5, 7, ...\ .\\\\a_2\ -\ a_1\ =\ d\\\\7\ -\ 5\ =\ 2\\\\\\The\ common\ difference\ is\ \bf 2.$

Answer 2

Given:

$\sf{ S_{1} = 5}$

$\sf{ S_{2} = 12}$

According to the question we have to

find The common difference ( d )

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$\sf{ S_{1} = a_{1}= 5}$ , the first term.

Hence, the first term of the A.P. is 5.

$\sf{ S_{2} = a_{2} = 12}$

→ 12 − 5 = 7

The second term is 7.

Therefore, the required A.P. is 5,7, - - -

a2 - a1 = d ( common difference)

→7 − 5 = 2

Hence, The common difference is 2.