Question

If the fourth term of an a.P. Is 4, then what is the sum of its first seven terms?

Answer 1

$a_{4} = a + 3d = 4$
$s_{7} = \frac{7}{2} (a + l) \\ s_{7} = \frac{7}{2} (a + a + 6d) \\ s_{7} = 7(a + 3d) \\ s_{7} = 7 \times 4 = 28$
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Answer 2

The sum of seven terms is 28.

Step-by-step explanation:

Given : If the fourth term of an A.P. is 4.

To find : What is the sum of its first seven terms?

Solution :

The A.P is in form $a,a+d,a+2d,a+3d,a+4d,.....$

The fourth term is $a_4=a+3d=4$ .....(1)

The sum of n term is given by

$S_n=\frac{n}{2}[2a+(n-1)d]$

The sum of 7 terms is

$S_7=\frac{7}{2}[2a+(7-1)d]$

$S_7=\frac{7}{2}[2a+6d]$

$S_7=\frac{7}{2}\times 2(a+3d)$

Substitute from equation (1),

$S_7=\frac{7}{2}\times 2(4)$

$S_7=7\times 4$

$S_7=28$

Therefore, the sum of seven terms is 28.

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If the fourth of an A.P is 4,then what is the sum of its 7 terms

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