Question

Find the 19 th term of an 7,13,19,25..​

Answer 1

Answer:

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Answer 2

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

Given series is 7, 13, 19, 25, -----

$\rm \: a_1 = 7$

$\rm \: a_2 = 13$

$\rm \: a_3 = 19$

$\rm \: a_4 = 25$

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$\rm \: a_2 - a_1 = 13 - 7 = 6$

$\rm \: a_3 - a_2 = 19 - 13 = 6$

$\rm \: a_4 - a_3 = 25 - 19 = 6$

It implies, the given series forms an AP series, with

First term, a = 7

Common difference, d = 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,

$\rm \: a_{19}$

$\rm \: = \: a + (19 - 1)d$

$\rm \: = \: a +18d$

$\rm \: = \: 7 +18 \times 6$

$\rm \: = \: 7 +108$

$\rm \: = \: 115$

Hence,

$\rm\implies \: \: a_{19} \: = \: 115$

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ADDITIONAL INFORMATION

Wᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ,

↝ 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.