Question

find the A.P. whose nth term is 7-3n.Also find the 20th term

Answer 1

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Answer 2

Answer:

-53 is  the value of  20th term  and A.P is 4, 1, ,-2,-5,-8......

Step-by-step explanation:

Explanation :

Given that , nth term is 7-3n .

Therefore , $T_{n}$ = 7-3n

Now , we put the values one by one 1,2,3,4,5, ....... in place of n we get

Step 1:

We have   $T_{n}$= 7-3n,

⇒$T_{1} = 7 - 3 (1) = 4$

⇒$T_{2} = 7 - 3 (2) = 1$

⇒$T_{3} = 7 - 3 (3) = -2$

⇒$T_{4} = 7 - 3 (4) = -5$

⇒$T_{5} = 7 - 3 (5) = -8$

$T_{20} = 7 - 3 (20) = -53$

So the A.P is  , 4, 1, -2 , -5 ,-8 ..........

∴ 1 - 4 = -3 , -2-1= -3 , -5-(-2 )= -5+2= -3 .

 So , the common difference is -3

and first term is 4 ,

From the A.P formula $a_{n} = a_{1}+ (n-1)d$

Now , put the value of first term ,common difference  and value of nth term  in the above equation we get ,

$a_{20} = 4+ (20-1)(-3)$

     = 4 - 57 = -53

Final answer :

Hence , 4, 1, -2, -5, -8 ...... is the A.P and value of 20th term is -53

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