Question

the nth of AP is 7-3n and then its common difference is​

Answer 1

Answer:

nth term is 7_3n and common difference is _3

Answer 2

The common difference of an AP(d) = - 3

Step-by-step explanation:

Given,

The nth term of AP ($a_{n}$) = 7 - 3n

To find, the common difference (d) of an AP = ?

Put n = 1, 2, 3, 4, 5, 6, ......, n

The 1st term of AP ($a_{1}$)

= 7 - 3(1) = 7 - 3 = 4

The 2nd term of AP ($a_{2}$)

= 7 - 3(2) = 7 - 6 = 1

The 3rd term of AP ($a_{3}$)

= 7 - 3(3) = 7 - 9 = - 2

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We know that,

Common  difference(d) = Second term ($a_{2}$) - First tern($a_{1}$)  = Third term($a_{3}$)  - second term($a_{2}$)

∴  Second term ($a_{2}$) - First tern($a_{1}$) = 1 - 4 = - 3

Third term($a_{3}$)  - second term($a_{2}$) = - 2 - 1 = - 3

∴ Common  difference(d) = - 3

Thus, the common difference of an AP(d) = - 3