Question

ɪғ ᴛ5=>11, ᴛ9=> 7, ᴛʜᴇɴ ᴛ16=> ?

ᴅᴏɴ'ᴛ ᴛʀʏ ᴛᴏ sᴘᴀᴍᴍɪɴɢ

Answer 1

Hello there!

Topic: Arithmetic Progression.

Thank you!

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Given Data:

T₅ = 11
T₉ = 7
T₁₆ = ? (to be find)

Formula going to be used: (Arithmetic Progressions)

To find nth number of the series, the formula is Tₓ = a + (n-1) d
where,
a is the first term of the series
d is the common difference between two consecutive terms.
n is the position of the term.

Solution:

Using Tₓ = a + (n-1) d, we will obtain two equation by following the data given.

Case 1: T₅ = a + (5-1)d              [as T₅=11]
             11 = a + 4d. or a + 4d = 11 ---------------   1

Case 2: T₉ = a + (9-1)d              [as T₉=7]
              7  = a+8d or a+8d = 7    ---------------- 2

Solving equations 1 and 2, we get   
[ multiply eqn 2 with minus for easy solving]

 a + 4d = 11
-a - 8d = -7
_________
    - 4d = 4
_________

d = -1  [common difference]

Substitute the d value in eqn 1 or 2:

a + 4(-1) = 11
a = 11+4 = 15 
a = 15 [starting value]

To find T₁₆ :

T₁₆ = a + (16-1)d
     = 15 + 15(-1)
     = 0

Therefore, 16th term of the arithmetic series (T₁₆) is 0.