Question

The fourth term of Ap is equal to 3 times it's first term and seventh term exceeds twice the third term by 1. find first term and common difference​

Answer 1

FINAL ANSWER:-

• hence first term (a) ⇒ 3

• common difference​ (d) ⇒ 2

GIVEN:-

• the fourth term of Ap is equal to 3 times it's first term

• seventh term exceeds twice the third term by 1

TO FIND:-

first term and common difference​

FORMULAS USED:-

basic arthmetic progression equations

SOLUTION:-

$1^{st}\:term=a\\3^{rd}\:term=a+2d\\4^{th}\:term=a+3d\\7^{th}\:term=a+6d$

so  

according to question

$4^{th}\:term=3(1^{st}\:term)$ ⇒ $a+3d=3(a)$ ⇒ $a+3d=3a$ ⇒ $3a-a-3d=0$ ⇒ $2a-3d=0...(1)$

and

$7^{th}\:term=2(3^{rd}\:term)+1$ ⇒ $a+6d=2(a+2d)+1$ ⇒ $a+6d=2a+4d+1$ ⇒$2a-a+4d-6d+1=0$ ⇒ $a-2d+1=0...(2)$

let be $a=2d-1...(3)$

and putting eq(2)  in equation 1 we get  

$2(2d-1)-3d=0$ ⇒ $4d-2-3d=0$ ⇒ $4d-3d-2=0$ ⇒ $d-2=0$ ⇒ $d=2$

now as we got the value of d so lets put in eq3 in order to get 'a' value

$a=2d-1$ ⇒ $a=2(2)-1$ ⇒ $a=4-1$  ⇒ $a=3$

hence first term (a) ⇒ 3

and

common difference​ (d) ⇒ 2

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Answer 2

Step-by-step explanation:

hey here is your answer in above pics

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