Question

In an arithmetic progression, if
$a_{6} \: = 17 \: and \: a_{3} \: = 8.$
then find the common difference and first term of the arthimetic progression.
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Answer 1

Answer:

common difference is 3 and first term of ap is 2

Answer 2

Answer:

• Common difference = 3
• First term = 2

Step-by-step explanation:

Given :

• sixth term, a₆ = 17
• third term, a₃ = 8

To find :

the common difference and first term of the A.P.

Solution :

In an A.P.,

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

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

where

a denotes first term

d denotes common difference

Sixth term = 17 :

Put n = 6,

a₆ = a + (6 - 1)d

17 = a + 5d ... eqn. [1]

Third term = 8 :

Put n = 3,

a₃ = a + (3 - 1)d

8 = a + 2d ... eqn. [2]

Subtract equation [2] from equation [1],

17 - 8 = a + 5d - (a + 2d)

 9 = a + 5d - a - 2d

 9 = 3d

 d = 9/3

 d = 3

∴ Common difference = 3

Substitute d = 3 in equation [2],

8 = a + 2d

8 = a + 2(3)

8 = a + 6

a = 8 - 6

a = 2

∴ First term = 2