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Question

Write the first term, common difference and nth term of A.P.
A.P.First term Common difference nth term
(i)-2,2,6,10, ......
(ii)13,53,93,133, .....

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Solution

An A.P has same difference between
any two comsecutive terms called the
common difference of the A.P
Formula for nth term, an of an A.P is
gicen by, an=a+(n1)d where a is
the first term and d is the common
difference. Hence we would get
(i)2,2,6,10
a=2;d=2(2)=4
an=2+(n1)4=2+4n4=4n6
(ii)13,53,93,133,....
a=13;d=5313=43
an=13+(n1)43=13+4n343=4n31
Derivation of an
We can write terms of an A.P as :
a,a+d,a+2d,a+3d,...
(From the property mentioned at the begining)
Therefore, we can see a pattern to write
any nth term as an=a+(n1)d.

1052447_1174281_ans_1eda3ee37c2d43429ed631d57dd78962.png

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