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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

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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 = 684\dfrac{68}{4}

⇒ n = 17.

Hence, there are a total of 17 terms in the progression.

(c) Since, n = 17, is odd.

By formula,

Middle term = n+12\dfrac{n + 1}{2}

= 17+12\dfrac{17 + 1}{2}

= 182\dfrac{18}{2}

= 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.

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