Question

the first term of an AP is 6 and the common difference is 5 .find its general term​

Answer 1

Answer:

General term of given AP is (5n + 1),

where n = 1, 2, 3, 4, 5, .....

Step-by-step explanation:

•First term of an AP , a = 6

•Common difference , d = 5

We know, general sequance of arithmetic progression is ; a , a + d, a + 2d, a + 3d....

So, A.P is ; 6, (6 + 5), (6 + 2 × 5), (6 + 3 × 5), .....

⇒AP is ; 6, 11, 16, 21, .....

$general \: term = a_{n} = a + (n - 1)d$

$a _{n} = a + (n - 1)d \\ </p><p> \: \: = 6 + (n - 1)5 \\ </p><p> \: \: = 6 + 5n - 5 \\ </p><p> \: \: = 5n + 1 \\ </p><p>$

So, general term of given AP is (5n + 1), where n = 1, 2, 3, 4, 5, .....

You can verify it,

First term ,

$a_{1}</p><p> </p><p> = 5 × 1 + 1 = 6$

2nd term ,

$a_{2}</p><p> = 5 ×2 + 1 = 11$

3rd term ,

$a_{3}= 5 × 3 + 1 = 16$

4th term ,

$a_{4}= 5 × 4 + 1 = 21$

............

Hence,

AP is ; 6, 11, 16, 21....

.

.

Hope it helps!(◕ᴗ◕✿)

Answer 2

Answer:

general term= 5n-1

Step-by-step explanation:

general term= an = a+(n-1)d = 6+(n-1)5 = 6+5n-5 = 5n-1