Question

In an ap first term is 2 last term is 29 and sum of its all term is 155 find d

Answer 1

Answer,

Here, first term = a = 2

Let the Common difference = d

Last term =  29

Sum of all terms = Sn = 155

Let there be n terms in the AP.

Now, Sum of n terms of this arithmetic series is given by:

Sn = n/2 [2a + (n-1) d ]

n / 2 [a + a + (n -1 ) d ]

n/2 [a + l]

Therefore sum of n terms of this arithmetic series is given by:

∴ Sn = n /2  [2 + 29] = 155

⇒ 31n = 310

⇒ n = 10

∴ there are 10 terms in the AP.

Thus ,
29 be the 10th term of the AP.

∴ 29 = a + (10 - 1)d

⇒ 29 = 2 + 9d

⇒ 27 = 9d

⇒ d = 3

∴ common difference = d =3

Hence,

d (Common difference) = [3]

Thanks!

Answer 2

Step-by-step explanation:

If a =2,an=29,Sn=155and d=?