Question

The sum of the first three terms of an A.P is 42 & the product of the first and the third term is 52. Find first term and common difference.

Answer 1

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Answer 2

The first term is 14.

The common difference is 12 or -12.

Step-by-step explanation:

Given : The sum of the first three terms of an A.P is 42 & the product of the first and the third term is 52.

To find : First term and common difference ?

Solution :

Let the three terms of A.P be 'a-d,a,a+d'.

The sum of the first three terms of an A.P is 42.

i.e. $a-d+a+a+d=42$

$3a=42$

$a=\frac{42}{3}$

$a=14$

The first term is 14.

The product of the first and the third term is 52.

i.e. $(a-d)(a+d)=52$

$a^2-d^2=52$

Put value of a,

$(14)^2-d^2=52$

$196-d^2=52$

$d^2=196-52$

$d^2=144$

$d=\sqrt{144}$

$d=\pm12$

The common difference is 12 or -12.

#Learn more

If the first term of an A.P if twice the common difference and its fourth

term is 5. Find the common difference

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