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.
- 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.
- Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.
- 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.
- The 5th term of an AP is 22 and its 9th term is six times the 2nd term. Find that AP.
- 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 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.
- 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.
Kickstart Your Career
Get certified by completing the course
Get Started