Question

LESSON :Arthematic progression
Class:10

1. 6th term of an Ap is -10 and 10th term is -26, find it's 15th term.​

Answer 1

Answer:

$\bigstar{\bold{The\:fifteenth\:term(a_{15})=-46}}$

Explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• 6th term of the A.P (a₆) = -10
• 10th term of the A.P (a₁₀) = -26

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• The 15th term (a₁₅) of the A.P

$\Large{\underline{\underline{\bf{Solution:}}}}$

$\dag$ Here we have to first find the common difference and first term (a₁) of the A.P.

$\dag$ The nth term of an A.P is given by,

  $\sf{a_n=a_1+(n-1)\times d}$

$\dag$ The 6th term of the A.P is given by

  a₆ = a₁ + ( 6 - 1 ) × d

 -10 = a₁ + 5d------(1)

$\dag$ The 10th term of the A.P is given by

  a₁₀ = a₁ + (10 - 1) × d

 -26 = a₁ + 9d --------(2)

$\dag$ Solving equation 1 and 2 by elimination method,

  a₁ + 5d = -10

  a₁ + 9d = -26

         -4d = 16

             d = 16/-4

             d = -4

$\dag$ Hence the common difference of the A.P is -4.

$\dag$ Substitute the value of d in equation 1

  a₁ + 5 × -4 = -10

  a₁ + -20 = -10

  a₁ = -10 + 20

  a₁ = 10

$\dag$ Hence the first term of the A.P is 10

$\dag$ Now the 15th term of the A.P is given by,

 a₁₅ = a₁ + (15 - 1) × d

 a₁₅ = a₁ + 14 d

$\dag$ Substituting the values,

  a₁₅ = 10 + 14 × -4

  a₁₅ = 10 + -56

  a₁₅ = -46

$\dag$ Hence the 15th term of the A.P is -46.

$\boxed{\bold{The\:fifteenth\:term(a_{15})=-46}}$

$\Large{\underline{\underline{\bf{Notes:}}}}$

$\dag$ The nth term of an A.P is given by,

 $\sf{a_n=a_1+(n-1)\times d}$

$\dag$ The common difference of an A.P is given by,

  $\sf{d=a_2-a_1}$

  $\sf{d=\dfrac{a_m-a_n}{m-n} }$