Question

In an AP if d= -4, n=7, an =4 then find a

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full explanation

Answer 1

Gɪᴠᴇɴ :

• The nᵗʰ term of an arithmetic sequence is 4.

• The common difference (d) is - 4

• The number of terms, n = 7

Tᴏ Fɪɴᴅ :

• The first term (a) of the given sequence.

Cᴀʟᴄᴜʟᴀᴛɪᴏɴ :

Wᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ,

↝ nᵗʰ term of an arithmetic sequence is,

$\begin{gathered}\red\bigstar\:\:{\underline{\orange{\boxed{\bf{\green{a_n\:=\:a\:+\:(n\:-\:1)\:d}}}}}} \\ \end{gathered}$

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.

Tʜᴜs,

• ↝ nᵗʰ term of an arithmetic sequence is 4

So,

Using formula

↝ nᵗʰ term of an arithmetic sequence is,

${\bf{\green{a_n\:=\:a\:+\:(n\:-\:1)\:d}}}$

$\rm :\implies\:4 = a + (7 - 1) \times ( - 4)$

$\rm :\implies\:4 = a + 6 \times ( - 4)$

$\rm :\implies\:4 = a - 24$

$\longmapsto \: \begin{gathered}\:{\underline{\boxed{\bf{\blue{{\tt \: \: a \: = \: \: 28 }}}}}} \\ \end{gathered}$

Hence,

• first term of the sequence is 28.

Answer 2

Answer:

Gɪᴠᴇɴ :

The nᵗʰ term of an arithmetic sequence is 4.

The common difference (d) is - 4

The number of terms, n = 7

Tᴏ Fɪɴᴅ :

• The first term (a) of the given sequence.

Cᴀʟᴄᴜʟᴀᴛɪᴏɴ :

Wᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ,

↝ nᵗʰ term of an arithmetic sequence is,

★ aₙ=a+(n-1)d

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.

Tʜᴜs,

↝ nᵗʰ term of an arithmetic sequence is 4

So,

Using formula

↝ nᵗʰ term of an arithmetic sequence is,

aₙ=a+(n-1)d

:⟹4=a+(7-1)+(-4)

:⟹4=a+6×(-4)

:⟹4=a-24

⟼a=28

Hence,

• first term of the sequence is 28.

Step-by-step explanation:

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Warm regards:Kanika