+1 vote
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The fourth term of an arithmetic progression is 8. What is the sum of the first 7 terms of the arithmetic progression?

1. 7
2. 64
3. 56
4. cannot be determined
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As here we have 7 terms so we can assume the terms of the A.P. as :   a - 3d , a - 2d , a - d , a , a + d , a + 2d and a + 3d

Thus  sum of 7 terms of the A.P, =   (a - 3d) + (a - 2d) + (a - d) + (a) + (a + d) + (a + 2d) + (a - 3d)

=    7a

=    7(8)   =  56 [ As fourth term of A.P. = a = 8 is given in the question ]

Hence C) should be the correct answer.

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Best approach to solve this kind of problems..:)
$a+3d=8$ [since 4th term is 8]

sum of 7 terms = $\frac{n}{2}(2a + (n-1)d)$

$=\frac{7}{2}(2a + 6d) = \frac{7}{2}(a + 3d + a + 3d) = \frac{7}{2}(16) = 56$
answered by (74 points) 1 5