Arithmetic Progression (AP)
-
Find the 15th term of the AP: 109, 113, 117, 121 ...
-
The first term of an AP is 9, and the common difference is -3. Find the 10th term.
-
In an AP, the 6th term is 19 and the 14th term is 67. Find the common difference.
-
The sum of the first 109 terms of an AP is 9. If the first term is 19, find the common difference.
-
How many terms of the AP 6, 9, 12, ... sum to 290?
-
In an AP, the 4rd term is 12 and the 10th term is 25. Find the 18th term.
-
The angles of a triangle form an AP. The smallest angle is 35°. Find the other angles.
-
Find the sum of all integers between 100 and 230 divisible by 6.
-
In an AP, Sn = 2n2 + 2n. Find the first term and common difference.
-
In an AP, the 109th term is zero. Prove that the 9th term is triple the 19th term.
-
Three numbers in AP sum to 6. Their product is 290. Find the numbers.
-
If 4, 12, 10 are in AP, show that 2×12 = 4 + 10.
-
The sum of the first n terms of an AP is 25n² + 18n. Find the 35th term.
-
In an AP, S100 = S230 (100≠230). Prove S100+230 = 0.
-
Find 6 so that 2×6+1, 2, and 5×6+2 form an AP.
-
The digits of a three-digit number are in AP. Their sum is 2, and reversing the digits decreases the number by 330. Find the number.
-
A clock strikes hours (1 to 12). Total strikes in a 2 day period?
-
Salary increases by $400 annually. After 11 years, total earnings are $800000. Find the starting salary.
-
In an AP, a5 = 34 and a13 = 66. Find a22.
-
Prove that the sum of the first \( n \) terms of an arithmetic progression (AP) is given by: \[ \frac{n}{2} \left[ 2a + (n - 1)d \right] \]
-
Given an arithmetic progression (AP) with first term 𝑎 = 5 and common difference 𝑑 = 3, complete the table below using:
- The \(n-th\) term formula: \[ T_n = a + (n-1)d \]
- The sum of the first \(n\) term formula: \[ S_n = \frac{n}{2} \left[2a + (n+1)d \right] \]
n \( a_n \) \( S_n \) 2 _____ _____ 3 _____ _____ 4 _____ _____ 5 _____ _____ 6 _____ _____
Podijelite vježbu: