Question

IfthethirdtermofanAPis12andtheseventhtermis24,thenfindthe

10thtermofsameAP​

Answer 1

Correct  Question :

If the third term of an A.P is 12 and the seventh term is 24 , then find the 10th term of same A.P.

Answer:

10th term = 33

Step-by-step explanation:

Given,

• third term, a₃ = 12
• seventh term, a₇ = 24

To find,

• 10th term = ?

Solution,

nth term of an A.P. is given by,

$\underline{\boxed{\bf a_n=a+(n-1)d}}$

where

a is the first term

d is the common difference

• third term = 12

Put n = 3,

a₃ = a + (3 - 1)d

12 = a + 2d ---[1]

• seventh term = 24

Put n = 7

a₇ = a + (7 - 1)d

24 = a + 6d ---[2]

equation [2] - equation [1]

24 - 12 = a + 6d - (a + 2d)

 12 = a + 6d - a - 2d

  12 = 4d

    d = 12/4

     d = 3

Common difference, d = 4

Substitute in equation [1]

 a + 2d = 12

 a + 2(3) = 12

  a + 6 = 12

   a = 12 - 6

    a = 6

first term, a = 6

we have to find the 10th term

Put n = 10

a₁₀ = a + (10 - 1)d

a₁₀ = 6 + 9(3)

a₁₀ = 6 + 27

a₁₀ = 33

Therefore, 10th term = 33

Answer 2

Step-by-step explanation:

$\huge\sf\underline\blue{answer:}$

$\huge\bf\underline\red{given,}$

third term of an A.P = 12

seventh term of ans A.P = 24

$\huge\sf\underline\green{to find,}$

10 term of an A.P

$\huge\fcolorbox{black}{pink}{required formula}$

$nth \: term \: of \: an \: a.p \: = a + (n - 1)d$

where,

a = 1st term

d = common difference

$\huge\fcolorbox{black}{purple}{solution:}$

.: 12 = a+(3-1)d

12 = a+2d [let it be equation 1]

.: 24 = a+(7-1)d

24 = a+6d [let it be equation 2]

equation 2 - equation 1

24-12 = a+6d -[a+2d]

12 = a+6d-a-2d

12 = 4d

d= 12/4 = 3

.: common difference (d) = 3.

substituting value of d in equation 1.

12 = a+2(3)

12 = a+6

a = 12-6 = 6

.: first term(a) = 6.

now,

10th term of an A.P =

a+(10-1)d

a+9d

6+9(3)

6+27

33

.: tenth term of an A.P = 33.