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

Answer:

Step-by-step explanation:

Answer 2

As it is given than S3=42

Let the first term be a

Let the the third term be a3

they given that product of-

a*a3=52

Firstly we apply the formula of sum of 3 no S3

S3=n/2(2a+(n-1)d

42=3/2(2a+2d)

42=3/2*2(a+d). taking 2 common from (2a+2d)

42=3(a+d)

42/3=a+d

14=a+d.......(1).

14-d=a

a(a+2d)=52

putting a value here

(14-d)(14-d+2d)=52

(14-d)(14+d)=52. (a+b)(a-b)=a²-b²

14²-d²=52

196-d²=52

-d²=52-196

-d²=-144

d²=144

d=12... putting this d value in eq(1)

14=a+d

14=a+12

14-12=a

2=a..

Hence common difference=12

First term a=2

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