Question
How many terms are there in the A.P.?
$7, 13, 19, ....., 205.$
$7, 13, 19, ....., 205.$
✓
Answer
Given,A.P. $7, 13, 19, ....., 205$
Here,
First term, $a =7$,
Difference $d=13-7=6$
Last $n ^{\text {th }}$ term $a _{ n }=205$
We know, $n ^{\text {th }}$ term of A.P.
$a_n=a+(n-1) d$
$\Rightarrow 205=7+(n-1) 6$
$\Rightarrow 205=7+6 n-6$
$\Rightarrow 205=1+6 n$
$\Rightarrow 6 n=204$
$\Rightarrow n=\frac{204}{6}$
$\Rightarrow n=34$
Hence, Total $34$ terms in given A.P.
Here,
First term, $a =7$,
Difference $d=13-7=6$
Last $n ^{\text {th }}$ term $a _{ n }=205$
We know, $n ^{\text {th }}$ term of A.P.
$a_n=a+(n-1) d$
$\Rightarrow 205=7+(n-1) 6$
$\Rightarrow 205=7+6 n-6$
$\Rightarrow 205=1+6 n$
$\Rightarrow 6 n=204$
$\Rightarrow n=\frac{204}{6}$
$\Rightarrow n=34$
Hence, Total $34$ terms in given A.P.
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