Question

Find no. of terms of ap if sum of 3,7,11 .......is 210

Answer 1

a=3,d=4

210=n/2(a+l)

210=n/2[2a+(n-1)d]

210=n/2[6+4n-4]

210=n/2[4n+2]

210=4n^2+2n/2

210=2(2n^2+n)/2

210=2n^2+n

0=2n^2+n-210

2n^2+(21-20)n-210=0

2n^2+21n-20n-210=0

2n^2-20n+21n-210=0

2n(n-10)+21(n-10)=0

(n-10)(2n+21)=0

n-10=0

n=10

2n+21=0

2n=-21

n= -21/2

Second answer is wrong because the value of n neither be in negative nor be in fraction.

So the value of n is 10 ...

Hope it helps you

Answer 2

Answer:

Step-by-step explanation:

In a Given A.P ;

a = 3

d = 7-3 = 4

On the contrary let 144 be the nth term of A.P

Tn = 144

n = ?

Tn = a+(n-1)d

144 = 3+(n-1)4

n-1 = 141/4

n = 35.25+1

n = 36.25

As the value of n is a decimal or number, hence 144 is not the term of given A.P