Question

Hi everyone

if the first ,second and seventh term of A.P are in G.P. and common difference is 2, the 2nd term of A.P is

Plz. reply CORRECTLY and in DETAIL, STEP BY STEP.​

Answer 1

Answer:

Step-by-step explanation:

let first term of A.P=a and common difference=d

so second term=a+d

seventh term=a+6d

according to question 1st,2nd and 7th term of A.P are in G.P

we know that if a,b,c are in G.P then b2=ac

⇒(a+d)2=a(a+6d)

⇒a2+2ad+d2=a2+6ad

⇒d2=4ad

⇒d=4a

here d=2

so 4a =2

⇒a=24

⇒a=12

Second term of A.P=a + d

⇒12+2

second term=52

Hope it helps u mark as brainliest please

Answer 2

Answer:

5/2

Step-by-step explanation:

AP:

First term = a.

Second term = a + d.

Seventh term = a + 6d.

G.P:

(a)(a + 6d) = (a + d)²

⇒ a² + 6ad = a² + d² + 2ad

⇒ a² + 6ad - a² - d² - 2ad = 0

⇒ -d² + 4ad = 0

⇒ -d² = -4ad

⇒ d² = 4ad

⇒ a = (d/4)

⇒ a = 2/4

⇒ a = 1/2

Now,

2nd term of A.P

= a + d

= (1/2) + 2

= 5/2

Therefore, 2nd term of A.P is (5/2).

Hope it helps!