fox and ßare the roots ofx2 + 5x-1-othen find(ii) α2+ β2There are 3

1.	fox and ßare the roots ofx2 + 5x-1-othen find(ii) α2+ β2There are 37 terms in an A.P. the sum of three terms plaexactly at the middle is 225 and the sum of last three term429. Write the A.P
Answer» Let the first term and the common difference of the A.P areaanddrespectively. Since the A.P contains 37 terms. So, the middle most term is (37+1)/2 th term = 19thterm. Thus, three middle most terms of this A.P.are 18th, 19thand 20thterms. Givena18+a19+a20= 225 ⇒ (a+ 17d) + (a+ 18d) + (a+ 19d) = 225 ⇒ 3(a+ 18d) = 225 ⇒a+ 18d= 75 ⇒a= 75 – 18d… (1) According to given information a35+a36+a37= 429 ⇒ (a+ 34d) + (a+ 35d) + (a+ 36d) = 429 ⇒ 3(a+ 35d) = 429 ⇒ (75 – 18d) + 35d= 143 ⇒ 17d= 143 – 75 = 68 ⇒d= 4 Substituting the value ofdin equation (1), it is obtained a= 75 – 18 × 4 = 3 Thus, the A.P. is 3, 7, 11, 15 …

fox and ßare the roots ofx2 + 5x-1-othen find(ii) α2+ β2There are 37 terms in an A.P. the sum of three terms plaexactly at the middle is 225 and the sum of last three term429. Write the A.P

Answer»

Let the first term and the common difference of the A.P areaanddrespectively.

Since the A.P contains 37 terms. So, the middle most term is (37+1)/2 th term = 19thterm.

Thus, three middle most terms of this A.P.are 18th, 19thand 20thterms.

Givena18+a19+a20= 225

⇒ (a+ 17d) + (a+ 18d) + (a+ 19d) = 225

⇒ 3(a+ 18d) = 225

⇒a+ 18d= 75

⇒a= 75 – 18d… (1)

According to given information

a35+a36+a37= 429

⇒ (a+ 34d) + (a+ 35d) + (a+ 36d) = 429

⇒ 3(a+ 35d) = 429

⇒ (75 – 18d) + 35d= 143

⇒ 17d= 143 – 75 = 68

⇒d= 4

Substituting the value ofdin equation (1), it is obtained

a= 75 – 18 × 4 = 3

Thus, the A.P. is 3, 7, 11, 15 …