Given: The arithmetic progression 5, 2, -1, -4, .........., -31

To find: The 6th term of the Arithmetic Progression.

Solution:

• Now we have given the arithmetic progression 5, 2, -1, -4, .........., -31.

• The first term a is 5.

• The common difference is 2 - 5 = -4 - (-1) = -3.

• The last term is -31.

• Now the sixth term of the Arithmetic Progression will be:

              a + 5d

• So putting the values in the sixth term, we get:

              5 + 5(-3)

              5 - 15

              -10

Answer:

                So the sixth term of the arithmetic progression 5, 2, -1, -4, .........., -31 is -10.

Let, a1=5, a2=2, a3 = -1 and an= -31

so d= a2 -a1=2-5= -3

then the nth term => an =a+(n-1)×d

=> -31= 5+(n-1)× -3

=> -31=5-3n+3

=> -3n= -31-8

=> n= -39/-3

=> n=13

so there are 13 term given AP

the 6th term from the end will be the 8th term

=> a8=a+(n-1) ×d

=> a8=5+(8-1) × -3

=> a8=5+7× -3

=> a8 = -16

the 6th term from the last term is -16

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