In the following APs, find the missing terms : (i) 2, ......, 26. (ii) ......, 13, ......, 3. (iii) 5, ......, ......., (iv) -4, ......, ....., ....., ......, 6 (v) ......, 38, ......, ....., ......, -22

Question

KnowledgeBoat · Accepted Answer

(i) Let x be the missing term. A.P. : 2, x, 26 Since, above list is in A.P. so common difference will be equal among consecutive numbers. ∴ x - 2 = 26 - x ⇒ x + x = 26 + 2 ⇒ 2x = 28 ⇒ x = = 14. Hence, missing term = 14. (ii) Let x and y be the missing term. A.P. : x, 13, y, 3. Since, above list is in A.P. so common difference will be equal among consecutive numbers. ∴ 3 - y = y - 13 ⇒ y + y = 13 + 3 ⇒ 2y = 16 ⇒ y = ⇒ y = 8. Common difference (d) : y - 13 = 8 - 13 = -5. ⇒ 13 - x = d ⇒ 13 - x = -5 ⇒ x = 13 + 5 = 18 Hence, missing terms are 18 and 8. (iii) Let x and y be the missing term. A.P. : 5, x, y, In above A.P., First term (a) = 5 Fourth term (a₄) = By formula, a_n = a + (n - 1)d In above A.P. x = 2nd term = a + d = . y = 3rd term = a + 2d = = 5 + 3 = 8. Hence, missing terms are . (iv) By formula, a_n = a + (n - 1)d First term (a) = -4 Sixth term (a₆) = 6 ⇒ a + (6 - 1)d = 6 ⇒ -4 + 5d = 6 ⇒ 5d = 6 + 4 ⇒ 5d = 10 ⇒ d = = 2. Second term = a + d = -4 + 2 = -2 Third term = a + 2d = -4 + 4 = 0 Fourth term = a + 3d = -4 + 6 = 2 Fifth term = a + 4d = -4 + 8 = 4 Hence, the missing terms are -2, 0, 2, 4. (v) By formula, a_n = a + (n - 1)d Let the first term be a and common difference be d. Given, Second term = 38 ⇒ a + (2 - 1)d = 38 ⇒ a + d = 38 ....(1) Given, Sixth term = -22 ⇒ a + (6 - 1)d = -22 ⇒ a + 5d = -22 ....(2) On Subtracting equation (1) from equation (2), we get : ⇒ a + 5d - (a + d) = -22 - 38 ⇒ a - a + 5d - d = -60 ⇒ 4d = -60 ⇒ d = = -15. Substituting value of d in equation (1), we get : ⇒ a + (-15) = 38 ⇒ a = 38 + 15 = 53. Third term = a₃ = a + (3 - 1)d = a + 2d = 53 + 2(-15) = 53 - 30 = 23. Fourth term = a₄ = a + (4 - 1)d = a + 3d = 53 + 3(-15) = 53 - 45 = 8. Fifth term = a₅ = a + (5 - 1)d = a + 4d = 53 + 4(-15) = 53 - 60 = -7. Hence, the missing terms are 53, 23, 8, -7.

Mathematics

In the following APs, find the missing terms : (i) 2, ......, 26. (ii) ......, 13, ......, 3. (iii) 5, ......, ......., (iv) -4, ......, ....., ....., ......, 6 (v) ......, 38, ......, ....., ......, -22

AP

Related Questions

Choose the correct choice in the following and justify :
30th term of the A.P. : 10, 7, 4, ….., is
97
77
-77
-87

Which term of the AP : 3, 8, 13, 18, ……., is 78 ?

Mathematics

In the following APs, find the missing terms : (i) 2, ......, 26. (ii) ......, 13, ......, 3. (iii) 5, ......, ......., (iv) -4, ......, ....., ....., ......, 6 (v) ......, 38, ......, ....., ......, -22

AP

Related Questions

Choose the correct choice in the following and justify :30th term of the A.P. : 10, 7, 4, ….., is9777-77-87

Which term of the AP : 3, 8, 13, 18, ……., is 78 ?

Choose the correct choice in the following and justify :
30th term of the A.P. : 10, 7, 4, ….., is
97
77
-77
-87