Question

In a Arithmetic Progression (A.P.) the fourth and sixth terms are 8 and 14 respectively. Find that:
(i) first term
(ii) common difference
(iii) sum of the first 20 terms. 

Answer 1

Let the first term of the sequence is a and the common difference is d. 

a₄ = a +3d = 8                    ...(1) 
a₆ = a + 5d = 14                 ...(2)  

       -      -         -
_______________________________
        -2d = - 6

            d = 3

Put d = 3 in equation (1)

a + 3 × 3 = 8

a = - 1

∴ (i) First term (a) = –1
   (ii) Common difference (d) = 3
  (iii) Sum of the first 20 terms = Sn `= n/2 [2a + (n-1)d]`

                               ` = 20/2 [2 xx (-1) + 19 xx 3]`

                               ` = 20/2 [-2+57]`

                                 = 10 × 55 = 550

Answer 2

Let the first term of the sequence is a and the common difference is d. 

a₄ = a +3d = 8                    ...(1) 
a₆ = a + 5d = 14                 ...(2)  

       -      -         -
_______________________________
        -2d = - 6

            d = 3

Put d = 3 in equation (1)

a + 3 × 3 = 8

a = - 1

∴ (i) First term (a) = –1
   (ii) Common difference (d) = 3
  (iii) Sum of the first 20 terms = Sn `= n/2 [2a + (n-1)d]`

                               ` = 20/2 [2 xx (-1) + 19 xx 3]`

                               ` = 20/2 [-2+57]`

                                 = 10 × 55 = 550

Answer 3

Let the first term of the sequence is a and the common difference is d. 

a₄ = a +3d = 8                    ...(1) 
a₆ = a + 5d = 14                 ...(2)  

       -      -         -
_______________________________
        -2d = - 6

            d = 3

Put d = 3 in equation (1)

a + 3 × 3 = 8

a = - 1

∴ (i) First term (a) = –1
   (ii) Common difference (d) = 3
  (iii) Sum of the first 20 terms = Sn `= n/2 [2a + (n-1)d]`

                               ` = 20/2 [2 xx (-1) + 19 xx 3]`

                               ` = 20/2 [-2+57]`

                                 = 10 × 55 = 550

Answer 4

Let the first term of the sequence is a and the common difference is d. 

a₄ = a +3d = 8                    ...(1) 
a₆ = a + 5d = 14                 ...(2)  

       -      -         -
_______________________________
        -2d = - 6

            d = 3

Put d = 3 in equation (1)

a + 3 × 3 = 8

a = - 1

∴ (i) First term (a) = –1
   (ii) Common difference (d) = 3
  (iii) Sum of the first 20 terms = Sn `= n/2 [2a + (n-1)d]`

                               ` = 20/2 [2 xx (-1) + 19 xx 3]`

                               ` = 20/2 [-2+57]`

                                 = 10 × 55 = 550

Answer 5

Let the first term of the sequence is a and the common difference is d. 

a₄ = a +3d = 8                    ...(1) 
a₆ = a + 5d = 14                 ...(2)  

       -      -         -
_______________________________
        -2d = - 6

            d = 3

Put d = 3 in equation (1)

a + 3 × 3 = 8

a = - 1

∴ (i) First term (a) = –1
   (ii) Common difference (d) = 3
  (iii) Sum of the first 20 terms = Sn `= n/2 [2a + (n-1)d]`

                               ` = 20/2 [2 xx (-1) + 19 xx 3]`

                               ` = 20/2 [-2+57]`

                                 = 10 × 55 = 550