The formula to find the nth term of an arithmetic progression is given by,an= a + ( n – 1 ) dwhere an = nth term,a = first term,n = position of the termd = common differenceNth Term of Arithmetic ProgressionThe formula an = a + ( n – 1 ) d is used to get the general...
The sum of first nn terms of an A.P. is 4n2+2n4n2+2n. To do: We have to find the nthnth term of the given A.P. Solution: Sn=4n2+2nSn=4n2+2n For n=1, S1=4×12+2×1=4+2=6n=1, S1=4×12+2×1=4+2=6 Therefore, first term a=6a=6 ...
Step 1: Write the formula for the nth term of an A.P.The nth term an can be calculated using the formula:an=Sn−Sn−1 Step 2: Substitute the expression for SnWe know:Sn=2n2+5nNow, we need to find Sn−1:Sn−1=2(n−1)2+5(n−1) Step 3: Expand Sn−1Now, let...
Each term can be expressed as: 0.7=710,0.77=77100,0.777=7771000,… The nth term can be expressed as: an=7⋯710n(n times 7) 2. Rewrite the series: Notice that: Sn=710+77100+7771000=710(1+0.1+0.01+…+0.1n−1) 3. Use the formula for the sum of a geometric series: The sum ...
The nth term of a sequence is given by an = 2n - 1. The sum of the first 5 terms S5 is _. A. 25 B. 30 C. 35 D. 40 相关知识点: 试题来源: 解析 A。解析:先根据通项公式求出前5项分别为1,3,5,7,9,再求它们的和为1 + 3 + 5 + 7 + 9 = 25。B选项计算错误,C选项...
Nth Term of Arithmetic Progression The general term (or)nthterm of an APwhose first term is 'a' and the common difference is 'd' is given by the formula an= a + (n - 1) d. For example, to find the general term (or) nthterm of the progression 6, 13, 20, 27, 34,. . . ...
结果1 题目 Find the sum of the first 15 terms of the sequence whose nth term is given by an = 2n - 1. A. 210 B. 225 C. 240 D. 255 相关知识点: 试题来源: 解析 B。解析:先求出通项公式,再用等差数列求和公式计算可得和为 225。 反馈 收藏 ...
days in a week or months in a year. this pattern of series and sequences has been generalized in maths as progressions. table of contents definition notation first term common difference general form nth term types of ap sum of nth term formula list questions and solutions problems to solve ...
And calculating the sum using formula will reduce the time to O(1). Also, the result can be huge so modulus of the values needs to be found. Let's derive the formula for nth term of the series, Tn=n2−(n−1)2Tn=n2−(n−1)2...
The ratio between consecutive terms in a geometric series is constant. We can write a formula for the nth term of a geometric series in the form {eq}a_n=ar^{n} {/eq}. When {eq}-1 < r < 1 {/eq}, the sum of ...