Question

Of 7th and 12th term of AP are 46 and 71 tespectively,find first 3 term​

Answer 1

Answer:

7th term of AP = 46

12th term of AP = 71

Formula for T(n) = a +(n-1)d

a+(7-1)d = 46

a+6d = 46 — (i)

a+(12-1)d = 71

a+11d = 71 — (ii)

Now, we compare equation (i) and (ii) using elimination method.

a + 6d = 46

a + 11d = 71

-5d = -25 (after subtraction)

d = 5

Now, we find value of ‘a’ by substituting the value of ‘d’ in equation (i).

a + 6(5) = 46

a + 30 = 46

a = 16

Since ‘a’ is the first term, we can now solve the rest of the problem.

a = 16

d = 5

First term = 16

Second term = 16+5

= 21

Third term = 21+5

= 26

_____________________________________________________________

VERIFY:

By substituting value of ‘a’ and ‘d’, we will check if the 7th and 12th term of AP is 46 and 71 respectively. If yes, then our answer is right.

⇒ a + 6d = 46

16 + 6(5) = 46

16 + 30 = 46

46 = 46

⇒ a + 11d = 71

16 + 11(5) = 71

16 + 55 = 71

71 = 71

Since both of our checks match, our answer is correct.

Hope it helps

Please mark my answer as BRAINLIEST

Answer 2

GIVEN:

• 7th term of an AP = 46
• 12th term of an AP = 71

TO FIND:

• What are the first three terms of an AP ?

SOLUTION:

Let the First term of an AP be 'a' and common difference be 'd'

According to question:-

✵ 7th term of an AP is 46.

✒ a + 6d = 46

✒ a = 46 –6d...1)

✵ 12th term of an AP is 71.

✒ a + 11d = 71...2)

Put the value of a from equation 1) in equation 2)

➸ 46 –6d + 11d = 71

➸ –6d + 11d = 71 –46

➸ 5d = 25

➸ d = $\sf{\cancel\dfrac{25}{5}}$

❮ d = 5 ❯

Put the value of d in equation 1)

➸ a = 46 –6 $\times$ 5

➸ a = 46 –30

❮ a = 16 ❯

First three terms of an AP are:-

◉ a = 16

◉ a + d = 16 + 5 = 21

◉ a + 2d = 16 + 2(5) = 16 + 10 = 26

❝ Hence, the first three terms of an AP are 16, 21, and 26 ❞

______________________