Question

find the sum of 51 terms of an A.P whose 2nd term is 2 and 4th term is 8​

Answer 1

Answer:

3774

Step-by-step explanation:

2nd Term of A.P = 2 => a + d = 2

4th term of the A.P = 8 => a + 3d = 8

By elimination method, equation(i) is subtracted from equation (ii)

(3d - d) = 8 - 2

2d = 6

d = 3

Therefore, a + d = 2

a = 2 - 3 = -1

S51 = n/2[2a + (n - 1)d]

= 51/2 [(2×-1) + (50×3)]

= 51/2 (150 - 2)

= (51 × 148) ÷ 2

= 51 × 74 = 3774

Answer 2

Required solution :

Here we're given with the 2nd term and 4th term of an A.P. and asked to calculate the sum of 51 terms.

As we know that nth term or general term of an A.P. is calculated by the formula :

• tn = a + (n - 1) d

Here,

• a is first term
• n is no. of terms
• d is common difference

Now, as we have :

• t_2 = 2
• t_4 = 8

>> 2 = a + (2 - 1) d

>> 2 = a + d → a = 2 - d

And,

>> 8 = a + (4 - 1) d

>> 8 = a + 3d (Equation No.1)

Substituting the value of "a" in Equation No.1 :

>> (2 - d) + 3d = 8

>> 2 - d + 3d = 8

>> 2 + 2d = 8

>> 2d = 8 - 2

>> 2d = 6

>> d = 3

Finding first term (a) :

>> a = 2 - d

>> a = 2 - 3

>> a = -1

As we know that sum of n terms of an A.P. is calculated by the formula :

• S = n/2 [2a + (n - 1) d]

We have :

• n = 51
• a = -1
• d = 3

Substituting the values :

→ S = 51/2 [2 (-1) + (51 - 1) 3]

→ S = 51/2 [2 (-1) + (50) 3]

→ S = 51/2 [2 × -1+ (50) 3]

→ S = 51/2 [-2 + (50) 3]

→ S = 51/2 [-2 + 50 × 3]

→ S = 51/2 [-2 + 150]

→ S = 51/2 [148]

→ S = 51 × 74

→ S = 3774