Find the nth term and sum of an arithmetic progression, and apply AP concepts to real-world sequence problems.
aₙ=a+(n-1)d, where a is the first term, d is the common difference, and n is the term number.
Find the 20th term of the AP 3, 8, 13, 18, ...
a=3,d=5; a₂₀=3+19×5=98
Find which term of the AP 2, 9, 16, ... is 149.
2+(n-1)×7=149; (n-1)×7=147; n-1=21; n=22
Find the 12th term of the AP 6, 11, 16, 21, ...
a=6,d=5; a₁₂=6+11×5=61
Sₙ=n/2×[2a+(n-1)d] gives the sum of the first n terms of an AP.
Find the sum of the first 15 terms of the AP 5, 8, 11, 14, ...
S₁₅=15/2×[10+14×3]=7.5×52=390
Find the sum of all multiples of 3 between 1 and 100.
AP: 3,6,...,99; n=33; S=33/2×(3+99)=33×51=1683
Find the sum of the first 12 terms of the AP 4, 7, 10, 13, ...
S₁₂=12/2×[8+11×3]=6×41=246
1. Find the 25th term of the AP 4, 9, 14, 19, ...
2. Find which term of the AP 5, 11, 17, ... is 89.
3. Find the sum of the first 20 terms of the AP 2, 5, 8, 11, ...
4. Find the sum of the first 10 multiples of 7.
5. How many terms of the AP 9, 17, 25, ... must be taken to give a sum of 636?
6. Find the 18th term of the AP 3, 7, 11, 15, ...
7. Find which term of the AP 3, 8, 13, ... is 123.
8. Find the sum of the first 25 terms of the AP 1, 4, 7, 10, ...
9. Find the sum of the first 15 odd numbers.
10. How many terms of the AP 5, 9, 13, ... add up to 324?