Question

–11, –7, –3, ............., 49, 53 are the terms of a progression.

Answer the following:

1. What is the type of progression?
2. How many terms are there in all?
3. Calculate the value of middle most term.

Answer 1

Given, –11, –7, –3, ............., 49, 53

a. 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 the first term (a) = −11 and the common difference (d) = 4.

Hence, the progression is an Arithmetic Progression.

b. Let 53 be the n^th term.

By formula,

t_n = a + (n – 1)d

53 = –11 + (n – 1)4

53 = –11 + 4n – 4

53 = –15 + 4n

4n = 53 + 15

4n = 68

n = `68/4`

n = 17

c. Since n = 17, is odd.

By formula,

Middle term = `(n + 1)/2`

= `(17 + 1)/2`

= `18/2`

= 9

Thus, 9^th term is the middle term.

By formula,

t₉ = a + (n − 1)d

= −11 + (9 − 1) × 4

= −11 + 8 × 4

= −11 + 32

= 21