Question

Which term of the Arithmetic Progression - 7,-12,-17,-22 will be -82 ? Is -100 any term of the A.P. ? Give reason for your answer.

Answer 1

Answer:

-82 will be the 16th term of the Arithmetic Progression

Step-by-step explanation:

The first term is, a = -7

The common difference will be, d = -12 - (-7) = -5

The nth term of an arithmetic progression is given by the formula,

Tₙ = a + (n-1)d

=> -82 = -7 + (n-1)(-5)

=> (n-1)(-5) = -75

=> n - 1 = 15

=> n = 16

Hence -82 will be the 16th term of the Arithmetic Progression.

Since these numbers are not a factor of 5, hence -100 will not be a term in the AP.

I hope this solution helps you. Please feel free to ask any doubts in the comment section.

Answer 2

answer : -82 is a term of given arithematic progression. but -100 isn't a term of given arithmetic progression.

we have to check that -82 is term of given arithmetic progression or not .

Arithmetic progression ; -7, -12, -17, -22.....

first term, a = -7 and common difference, d = -12 -(-7) = -12 + 7 = -5

nth term of given progression, $T_n=a+(n-1)d$

= -7 + (n - 1) × -5

= -7 - 5n + 5

= -2 - 5n ........(1)

take $T_n=-82$

or, -82 = -2 - 5n [ from equation (1), ]

or, -82 + 2 = -5n

or, -5n = -80 => n = 16

here, we get n is a positive integer. so, we can say that -82 is an arithmetic progression.

Let's check -100 is a term of given arithematic progression.

take $T_n=-100$

or, -100 = -2 - 5n [ from equation (1), ]

or, -100 + 2 = -5n

or, -5n = -98 => n = 98/5 {fractional}

here n is fractional so, -100 isn't a term of given arithematic progression.