-11, -7, -3, .......,49, 53 are the terms of a progression. Answer the following: (a) What is the type of progression? (b) How many terms are there in all? (c) Calculate the value of middle most term.

Question

KnowledgeBoat · Accepted Answer

(a) Given, -11, -7, -3, ......,49, 53 Second term - First term : −7 − (−11) = 4 Third term - Second term : −3 − (−7) = 4 Last term - Second last term : 53 − 49 = 4 Since the difference between consecutive terms is constant, the progression is an Arithmetic Progression (AP) with first term (a) = -11 and common difference (d) = 4. Hence, the progression is an Arithmetic Progression. (b) Let 53 be the nth term. By formula, ⇒ tn = a + (n - 1)d ⇒ 53 = -11 + (n - 1)4 ⇒ 53 = -11 + 4n - 4 ⇒ 53 = -15 + 4n ⇒ 4n = 53 + 15 ⇒ 4n = 68 ⇒ n = ⇒ n = 17. Hence, there are a total of 17 terms in the progression. (c) Since, n = 17, is odd. By formula, Middle term = = = = 9. Thus, 9th term is middle term. By formula, ⇒ t9 = a + (n - 1)d = -11 + (9 - 1) × 4 = -11 + 8 × 4 = -11 + 32 = 21. Hence, the value of the middle most term is 21.

Mathematics

-11, -7, -3, …….,49, 53 are the terms of a progression.
Answer the following:
(a) What is the type of progression?
(b) How many terms are there in all?
(c) Calculate the value of middle most term.

AP

Related Questions

P is a point on the x-axis which divides the line joining A(-6, 2) and B (9, -4). Find:
(a) the ratio in which P divides the line segment AB.
(b) the coordinates of the point P.
(c) equation of a line parallel to AB and passing through (-3, -2).

In the given figure AC is the diameter of the circle with center O. CD is parallel to BE.
∠AOB = 80° and ∠ACE = 20°. Calculate :
(a) ∠BEC
(b) ∠BCD
(c) ∠CED

Mathematics

-11, -7, -3, …….,49, 53 are the terms of a progression.Answer the following:(a) What is the type of progression?(b) How many terms are there in all?(c) Calculate the value of middle most term.

AP

Related Questions

P is a point on the x-axis which divides the line joining A(-6, 2) and B (9, -4). Find:(a) the ratio in which P divides the line segment AB.(b) the coordinates of the point P.(c) equation of a line parallel to AB and passing through (-3, -2).

In the given figure AC is the diameter of the circle with center O. CD is parallel to BE.∠AOB = 80° and ∠ACE = 20°. Calculate :(a) ∠BEC(b) ∠BCD(c) ∠CED

-11, -7, -3, …….,49, 53 are the terms of a progression.
Answer the following:
(a) What is the type of progression?
(b) How many terms are there in all?
(c) Calculate the value of middle most term.

P is a point on the x-axis which divides the line joining A(-6, 2) and B (9, -4). Find:
(a) the ratio in which P divides the line segment AB.
(b) the coordinates of the point P.
(c) equation of a line parallel to AB and passing through (-3, -2).

In the given figure AC is the diameter of the circle with center O. CD is parallel to BE.
∠AOB = 80° and ∠ACE = 20°. Calculate :
(a) ∠BEC
(b) ∠BCD
(c) ∠CED