Question

the sum of three terms of an AP is 42 and the product of the first and the third term is 52. Find the first term and the common difference.

I used 'a' as the first term, (a+d) as the second term and (a+2d) as the third term. Is this method correct to find the first term?

Solution

Sum= 43
n/2(2a+(n-1)d)=42
3/2(2a+2d)=42
a+a+2d=28
a+2d=28-a

Given
a(a+2d)=52
placing the value of (a+2d)
a(28-a)=52
28a-a^2=52
a^2-28a+52=0
a^2-26a-2a+52=0
a(a-26)-2(a-26)=0
(a-2)(a-26)=0
a=2;26. ANSWER​

Answer 1

answer of your question.

Answer 2

Let a - d , a , a + d are three consecutive terms in arithmetic progression.

a/c to question,

(a - d) + a + (a + d ) = 42

or, 3a = 42

or, a = 14..........(1)

again, (a - d) × (a + d) = 52

or, a² - d² = 52

or, (14)² - d² = 52

or, 196 - d² = 52

or, d² = 196 - 52 = 144

or, d = ± 12

hence, first term is (a - d) = 2 [ when d = 12 ] and 26 [ when d = -12 ]

so, first term, a = 2 when common difference, d = 12

first term, a = 26 when common difference , d = -12