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Question

If the first, second and last term of an A.P are a, b and 2a respectively, then its sum is



A

ab2(ba)

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B

abba

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C

3ab2(ba)

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D

None of these

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Solution

The correct option is C

3ab2(ba)


Let the A.P. be a, a + d, a + 2d ..... a + nd

Here, let d be the common difference and n be the total number of terms.

Given:

a1=a

a2=b

a+d=b

d=ba(1)

an=2a

a+(n1)d=2a

d=an1(2)

From equation (1) and (2), we have:

an1=ba

aba+1=n

bba=n

Now, sum of n terms of an A.P. :

S=n2{a+an}

=n2(3a)

=3ab2(ba)


Mathematics
RD Sharma
Standard XI

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