Question

if -42 is a term of a series 7+2-3+.............? give reasons

Answer 1

It is not a term of A.P. Because Value

of n is in fraction.

Hope it helps you dear.......xd

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

The ${n}^{th}$term of an Arithmetic progression is

$= a \: + (n - 1)d$

Where First term = a

Common Difference = d

CALCULATION

First term = a = 7

Common Difference = d = 2 - 7 = - 5

Let - 42 be the ${n}^{th}$term

So

$a + (n - 1)d \: = - 42$

$\implies \: 7 - 5(n - 1) = - 42$

$\implies \: - 5(n - 1) = - 49$

$\implies \: (n - 1) = \frac{49}{5}$

$\implies \: n = \frac{54}{5}$

So n is not a natural number

So - 42 is not a term of the AP