Question

find the nth term and the 20th term of the sequence 9,5,1,-3

Answer 1

Answer:

nth term =13-4n

20th term=67

Step-by-step explanation:

this is A. P.

formula is nth term=1st term+(n-1)d=9+(n-1)(-4)=9-4n+4=13-4n

d means common difference between two terms

Here, 1st term=9 ,d=common difference=-4

20th term=9+(20-1).(-4)=9+19*(-4)=9+(-76)=67

Answer 2

Required Solution :-

Here we've been given with an A.P. and firstly we need to calculate the nth term of it !

As we can clearly notice that we have first term (a) and common difference (d) of the A.P.

We have :

• First term (a) = 9
• Common difference (d) = 5 - 9 = -4

As we know that general term or nth term of an A.P. is calculated by the formula :

• tn = a + (n - 1) d

Here,

• a is first term
• n is no. of terms
• d is common difference

Substituting the values :

→ tn = 9 + (n - 1) -4

→ tn = 9 + (n - 1) × -4

→ tn = 9 - 4n + 4

→ tn = 13 - 4n

Therefore,

• nth term of the A.P. is (13 - 4n)

~ Calculating the 20th term of the A.P. :-

→ t_20 = 13 - 4 (20)

→ t_20 = 13 - 4 × 20

→ t_20 = 13 - 80

→ t_20 = -67

Therefore,

• 20th term of the A.P. is -67.