Find the sum of last ten terms of the AP: $ 8,10,12, \cdots, 126 $.
Given:
Given A.P. is $8, 10, 12, 14,…, 126$.
To do:
We have to find the sum of the last ten terms of the A.P.: $8, 10, 12, 14,…, 126$.
Solution:
For finding the sum of the last ten terms, we can write the given A.P. in reverse order.
This implies, the A.P. now becomes,
$126, 124,........, 14, 12, 10, 8$
Here,
First term \( (a)=126, \) common difference \( (d)=124-126=-2 \)
We know that,
${S}_{n}=\frac{n}{2}[2 a+(n-1) d]$
Therefore,
$\mathrm{S}_{10}=\frac{10}{2}[2 a+(10-1) d]$
$= 5[2(126)+9(-2)]$
$=5(252-18)$ $=5 \times 234$
$=1170$
The sum of the last ten terms of the A.P.: $8, 10, 12, 14,…, 126$ is $1170$.
Related Articles
- Find the sum of last ten terms of the A.P.: $8, 10, 12, 14,…, 126$.
- The sum of the first five terms of an AP and the sum of the first seven terms of the same AP is 167. If the sum of the first ten terms of this AP is 235 , find the sum of its first twenty terms.
- An AP consists of 37 terms. The sum of the three middle most terms is 225 and the sum of the last three is 429 . Find the AP.
- In an AP of 50 terms, the sum of first 10 terms is 210 and the sum of its last 15 terms is 2565. Find the A.P.
- In an A.P., the sum of first ten terms is -150 and the sum of its next ten terms is -550. Find the A.P.
- The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.
- Find the sum of first $16$ terms of the AP: $10,\ 6,\ 2\ .......$
- 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 sum of first 7 terms of an AP is 49 and that of 17 terms is 289. Find the sum of first n terms .
- The first and the last terms of an AP are 5 and 45 respectively. If the sum of all its terms is 400, Find its common difference.
- The first and the last terms of an AP are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.
- If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first $n$ terms.
- If sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256 , find the sum of first 10 terms.
- The sum of first 6 terms of an \( \mathrm{AP} \) is 36 and the sum of its first 16 terms is 256. Find the sum of first 10 terms of this \( A P \).
- The sum of how many terms of the AP \( 8,15,22, \ldots \) is \( 1490 ? \)
Kickstart Your Career
Get certified by completing the course
Get Started