Question

in an ap fourth and sixth term are 8 and 14 find first term, commom difference​

Answer 1

Given:-

• 4th term = 8
• 6th term = 14

To find:-

• 1st term
• Common difference (d)

Solution:-

We know

an = a + (n - 1) × d

For 4th term,

= a4 = a + (4 - 1) × d

= 8 = a + 3d

=> a + 3d = 8 ----------> (i)

For 6th term,

= a6 = a + (6 - 1) × d

= 14 = a + 5d

=> a + 5d = 14 ---------> (ii)

Subtracting eq. (i) from eq. (ii)

(a + 5d = 14) - (a + 3d = 8)

= a + 5d = 14

-a - 3d = - 8

2d = 6

=> d = 6/2

=> d = 3

Putting the value of d in eq. (i)

a + 3d = 8

=> a + 3×3 = 8

=> a + 9 = 8

=> a = 8 - 9

=> a = -1

Therefore,

First term (a) = -1

Common difference (d) = 3

Verification:-

an = a + (n-1) × d

a1 = -1 + (1-1) × 3

= -1 + 0×3

= -1

a4 = -1 + (4-1) × 3

= -1 + 3×3

= -1 + 9

= 8

a6 = -1 + (6-1) × 3

= -1 + 5×3

= -1 + 15

= 14

[Hence Verified].