Question

Which term of AP:6,2,-2.....is -146

Answer 1

-146 is the 39th term of the given AP.

Given:

an arithmetic progression: 6, 2, -2,...

To Find:

-146 is which term of the given AP

Solution:

let -146 be the nth term of the given AP

we know that the nth term of an AP is given as-

aₙ = a + (n - 1)d

where a = first term of the AP

d = common difference

here, a = 6

and d = (2 - 6) = -4

substituting the values of a and d into the formula we get-

aₙ = 6 + (n - 1)(-4)

aₙ = 6 - 4n + 4

aₙ = 10 - 4n

we know that aₙ = -146

⇒ -146 = 10 - 4n

-146 - 10 = -4n

4n = 156

n = 156/4

n = 39

Thus, -146 is the 39th term of the given AP.

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Answer 2

The 39th term of AP is -146.

Given:

AP:6,2,-2......

To Find:

Term number of -146.

Solution:

To find, which term is -146 we will follow the following steps:

As we know,

The term an AP is given by the formula:

$t = a + (n - 1)d$

t is the term i.e -146

n is the place at which -146 is in AP.

a = first number = 6

d is the common difference between two consecutive digits.

So,

d = 2 - 6 = -4

Now,

In putting values we get,

$- 146 = 6 + (n - 1) - 4$

$- 146 - 6 = (n - 1) - 4$

$\frac{ - 152}{ - 4} = n - 1$

$n - 1 = 38$

$n = 38 + 1 = 39$

Henceforth, the 39th term of AP is -146.

#SPJ3