Question

the last term of an AP of 'n' terms whose first term is 'x' and the common difference 'y' is​

Answer 1

using formula

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

given that

first term=x

common difference=y

then the last term is

$\huge{\mathcal{\boxed{\blue{An=x+(n-1)y}}}}$

Answer 2

Answer:

According to AP, the general term of an AP sequence is given as:

⇒ aₙ = a + ( n - 1 ) d

Where, 'aₙ' refers to the nth term, 'a' refers to the first term 'd' refers to the common difference of the AP and 'n' refers to the number of terms in the AP.

According to the question,

• aₙ = ?
• a = x
• d = y
• n = n

Therefore substituting in the equation we get,

⇒ aₙ = a + ( n - 1) d

⇒ aₙ = x + ( n - 1 ) y

Last term is n-1. Therefore the general equation of the last term is:

⇒ aₙ₋₁ = x + ( n - 2 ) y

This is the required equation.