Question

3) Find the 20th term of the given A. P. 7,13,19,25,..​

Answer 1

$\large\underline{\sf{Solution-}}$

Given AP series is 7, 13, 19, 25, ...

It means,

• First term of an AP, a = 7

• Common difference of an AP, d = 13 - 7 = 6

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,

$\rm \: a_{20}$

$\rm \: = \: a + (20 - 1)d$

$\rm \: = \: a + 19d$

$\rm \: = \: 7 + 19 \times 6$

$\rm \: = \: 7 + 114$

$\rm \: = \: 121$

Hence,

$\rm\implies \:\boxed{ \rm{ \:a_{20} = 121 \: }}$

$\rule{190pt}{2pt}$

Additional Information :-

↝ Sum of n  terms of an arithmetic sequence is,

$\begin{gathered}\red\bigstar\:\:{\underline{\orange{\boxed{\bf{\green{S_n\:=\dfrac{n}{2} \bigg(2 \:a\:+\:(n\:-\:1)\:d \bigg)}}}}}} \\ \end{gathered}$

Wʜᴇʀᴇ,

• Sₙ is the sum of n terms of AP.

• a is the first term of the sequence.

• n is the no. of terms.

• d is the common difference.

Answer 2

Step-by-step explanation:

Given AP series is 7, 13, 19, 25, ...

It means,

• First term of an AP, a = 7

• Common difference of an AP, d = 13 - 7 = 6

We know

↝ nᵗʰ term of an arithmetic sequence is,

$\large\boxed{\sf{ a_{n} =a + (n - 1)d }}$

,

$\large\underline{\sf{a_{n} \: is \: the \: {n}^{th } \: term }}$

• a is the first tem of the sequence.

• n is the number of terms.

• d is the common difference.

=13-7=6

Hence,

$\large\underline{\sf{ a_{20} = a + (20 - 1)d}}$

$\large\underline{\sf{a_{20} = a + 19d}}$

$\large\underline{\sf{ \implies a_{20} = 7 + 19 \times 6}}$

$\large\underline{\sf{ \implies 7 + 114}}$

$\large\underline{\bf{ \implies 121}}$

Hence the 20th term of the AP is 121