Question

determine the 50th term of an ap whose fifth term is 19 and the difference of 8th term from the 13th term is 20​

Answer 1

Step-by-step explanation:

Given :-

An AP whose fifth term is 19 and the difference of 8th term from the 13th term is 20.

To find :-

Find 50th term of the AP ?

Solution :-

Let the first term of an AP be 'a'

Let the common difference be 'd'

We know that

nth term of an AP = an = a+(n-1)d

Given that

5th term of an AP = 19

=>a5 = a+(5-1) d = 19

=> a + 4d = 19 ------------------(1)

The difference between 13th term and 8th term = 20

=> a 13 - a 8 = 20

=> [a+(13-1)d] -[a+(8-1)d] = 20

=> (a+12d)-(a+7d) = 20

=> a+12d-a-7d = 20

=> (a-a)+(12d-7d) = 20

=> 0 + 5d = 20

=> 5d = 20

=> d = 20/5

=> d = 4

Common difference = 4

On substituting the value of d in (1) then

=> a+4(4) = 19

=> a +16 = 19

=> a = 19-16

=> a = 3

First term = 3

Now,

50th term = a 50

=> a+(50-1)d

=> a+49d

=> 3+49(4)

=> 3 + 196

=> 199

Therefore, a 50 = 199

Answer:-

50th term of the given AP is 199

Used formulae:-

nth term of an AP = an = a+(n-1)d

a = First term

d = Common difference

n = Number of terms