Math, asked by palaparthisanjana, 16 days ago

for what value of nth term of two AP's 65,70,75 & 5,14, 23 are equal​

Answers

Answered by tennetiraj86
1

Step-by-step explanation:

Given :-

Two AP's 65,70,75 & 5,14, 23

To find :-

For what value of nth term of two AP's 65,70,75 & 5,14, 23 are equal ?

Solution :-

Given that :

First A P : 65,70,75,...

First term = a = 65

Common difference= d = 70-65 = 5

We know that

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

=> an = 65+(n-1)5

=> an = 65 + 5n -5

=> an = 65-5+5n

=> an = 60+5n

Therefore,nth rem of the first AP = 5n+60 -----(1)

Second AP :5,14,23,...

First term = a = 5

Common difference = d = 14-5 =9

We know that

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

=> an = 5+(n-1)9

=> an = 5 + 9n -9

=> an = 5-9+9n

=> an = (-4)+9n

Therefore,nth rem of the second AP = 9n-4 ---(2)

Let both nth terms are equal

=> (1) = (2)

=>5n +60 = 9n -4

=> 9n -5n = 60+4

=> 4n = 64

=> n = 64/4

=> n = 16

so, required value of nth term = 16th term

Answer:-

For 16th both given AP's are equal.

Check :-

16th term of the first AP :65,70,75,..

a 16 = a+15d

=> 65+15(5)

=> 65+75

=> 140

a 16 = 140

and

16th term of the second AP :5,14, 23

a 16 = a+15d

=> 5+15(9)

=> 5 + 135

=> 140

Both 16 th terms are equal

Verified the given relations in the given problem

Used formulae :-

  • nth term of an AP = an = a+(n-1)d

Where,

  • a = First term

  • d = Common difference

  • n = number of terms

Answered by mundadasachin
0

Answer:

For 16th both given AP's are equal.

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