Question

. The sum of the first 4 terms of an A.P is 26
and the sum of their squares is 214. Find
the first 4 terms.​

Answer 1

Step-by-step explanation:

sorry the remaining process you have to do.... it may useful for you.. for the nxt time..

Answer 2

Given:

✰ Sum of first 4 terms = S₄ = 26

✰ Sum of squares = 214

To find:

First 4 terms.

Method:

Let us assume that the first term of A.P is a and common difference is d

According to the question,

a + (a + d) + (a + 2d) + (a + 3d) = 26

⇒4a + 6d = 26

Dividing by 2 on both sides

⇒ 2a + 3d = 13. –––– (Equation 1)

Also,

(2a + 3d)² = (13)²

Using (a + b)² = a² + b² + 2ab

(2a + 3d)² = (2a)² + (3d)² + 2×2a×3d = 169

(2a + 3d)² = 4a² + 9d² + 12ad = 169

⇒4a² + 9d² + 12ad = 169 -– (Equation 2)

Now,

a² + (a + d)² + (a + 2d)² + (a + 3d)² = 214

⇒ a² + (a² + d² + 2ad) + (a² + 4ad + d²) + (a² + 9d² + 6ad) = 214

⇒ 4a² + 14d² + 12ad = 214 – (Equation 3)

(Equation 3) - (Equation 2)

4a² + 14d² + 12ad = 214

(-) 4a² + 9d² + 12ad = 169

5d² = 45

⇒d² = 45 ÷ 5

⇒ d² = 9

⇒ d = ±3

For d = -3

From Equation 1,

2a + 3d = 13

⇒2a + (-9) = 13

⇒ 2a - 9 = 13

⇒ 2a = 22

⇒ a = 11

A.P → 11, 8, 5, 2, ...

For d = 3

From Equation 1,

2a + 3d = 13

⇒2a + 9 = 13

⇒ 2a = 4

⇒ a = 2

A.P → 2, 5, 8, 11, ...