Question

which term of an a.p. -4,-1,2,.... is 101?

Answer 1

In this a.p.

a= -4

d = -1 - (-4)

d= -1+4

d = 3

let in this a.p. the nth term is 101

so

an = 101

a + ( n-1 ) d = 101

-4 + ( n - 1) 3 = 101

(n -1 ) 3 = 101 + 4

(n -1) 3 = 105

n - 1 = 105 / 3

n - 1 = 35

n = 35 + 1

n = 36

so we get

the 36th term of this a.p is 101.

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Answer 2

a=-4, d=-1-(-4)=3, an=101,n=?
an=a+(n-1)×d
101=-4+(n-1)×3
101+4=3n-3
105+3=3n
3n=108
n=36