An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.
Given:
An A.P. consists of 50 terms. The 3rd and the last terms are 12 and 106 respectively.
To do:
We have to find the 29th term.
Solution:
Let $a$ be the first term and $d$ be the common difference.
Number of terms $n=50$
3rd term $a_3=a+2d=12$........(i)
Last term $a_n=a+(n-1)d$
Therefore,
$a_{50}=a+(50-1)d=106$
$106=a+49d$.....(ii)
Subtracting (i) from (ii), we get,
$a+49d-a-2d=106-12$
$47d=94$
$d=\frac{94}{47}$
$d=2$
This implies,
$a+2(2)=12$
$a=12-4=8$
29th term $a_{29}=a+(29-1)d$
$=8+28(2)$
$=8+56$
$=64$
The 29th term is 64.
Related Articles
- Determine the AP whose 3rd term is 16 and 7th term exceeds the 5th term by 12.
- The first term of an AP is 12 and its 7th term is 24 less than its 11th term. Find the 20th term of this AP.
- If the 3rd and the 9th term of an AP are $4$ and $-8$ respectively, which term of this AP is zero?
- The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.
- Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.
- The first term of an AP is \( -5 \) and the last term is 45 . If the sum of the terms of the AP is 120 , then find the number of terms and the common difference.
- The 5th term of an AP is 22 and its 9th term is six times the 2nd term. Find that AP.
- The first term of an A.P. is 2 and the last term is 50. The sum of all these terms is 442. Find the common difference.
- Find the second term and nth term of an A.P. whose 6th term is 12 and the 8th term is 22.
- The sum of the 5th term and the 9th term of an \( \mathrm{AP} \) is 30 and the 25th term of the \( \mathrm{AP} \) is three times the 8th term. Find that AP.
- If 9th term of an A.P. is zero, prove that its 29th term is double the 19th term.
- The sum of 5th and 9th terms of an AP is 30. If its 25th term is three times its 8th term, find the AP.
- Which term of the AP: \( 53,48,43, \ldots \) is the first negative term?
- The first term of an A.P. is 5, the common difference is 3 and the last term is 80; find the number of terms.
- The sum of the 5th and the 9th terms of an AP is 30. If its 25th term is three times its 8th term, find the AP.
Kickstart Your Career
Get certified by completing the course
Get Started