Question

In an Arithmetic Progression, if d = - 2, n = 5, an (nth term) = 4, then a (first term) is​

Answer 1

d= -2

n=5

nth term=4

BY USING ABOVE FORMULA

4 = a + (5-1)(-2)

4 = a +4(-2)

a-8=4

a=12

Answer 2

$\sf\small{ \underline{\underline\red{ \pmb{ Given :-}}}}$

• d = -2
• n = 5
• aₙ = 4

$\sf\small{ \underline{\underline\red{ \pmb{To \: find :-}}}}$

• a (First term)

$\sf\small{ \underline{\underline\red{ \pmb{Formula \: \: used :-}}}}$

Wᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ,

↝ nᵗʰ term of an arithmetic sequence is,

$\red\bigstar\:\:{\underline{\purple{\boxed{\bf{\pink{a_n\:=a + (n - 1)}}}}}}$

Wʜᴇʀᴇ,

• aₙ is the nᵗʰ term.
• a is the first term of the sequence.
• n is the no. of terms.
• d is the common difference.

$\sf\small{ \underline{\underline\red{ \pmb{Solution :-}}}}$

$\sf a_n= a+(n-1) d$

$\sf \dashrightarrow 4= a+(5-1)( - 2)$

$\sf \dashrightarrow 4= a - 10 + 2$

$\sf \dashrightarrow 4 - 2= a - 10$

$\sf \dashrightarrow 2 = a - 10$

$\sf \dashrightarrow 2 + 10 = a$

$\sf \dashrightarrow a = 12$

The First term of this A. P. is 12.