In an ap sum of first n terms is 3n 2/2
WebThe sum of n terms of an AP can be found using one of the following formulas: S n = n/2 (2a+ (n−1)d) S n = n/2 (a 1 +a n) Here, a = a 1 = the first term, d = the common difference, n = number of terms, a n = n th term, S n … WebDec 19, 2024 · (iii) Sum of n terms of an AP is always quadratic in ‘n’ Example: S n = 2n 2 + 3n. Example: S n = n/4 (n + 1) we can find ‘d’ also from S n. d = 2 (coefficient of n 2) for eg. : 2n 2 + 3n, d = 2 (2) = 4 Verification: S n = 2n 2 + 3n at n = 1, S 1 = 2 + 3 = 5 = first term at n = 2, S 2 = 2 (2) 2 + 3 (2) = 8 + 6 = 14 ≠ second term
In an ap sum of first n terms is 3n 2/2
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WebIt is given that sum of the first n terms of an A.P. is 3n 2 + 6n. ∴ First term = a = S 1 = 3 (1) 2 + 6 (1) = 9. Sum of first two terms = S 2 = 3 (2) 2 + 6 (2) = 24. ∴ Second term = S 2 − S 1 = 24 − 9 = 15. ∴ Common difference = d = Second term − First term = 15 − 9 = 6 Also, n th term = a n = a + (n − 1)d ⇒ a n = 9 + (n − 1)6 ⇒ a n = 9 + 6n − 6 WebThe sum of the first n terms of an AP is (5n 2 /2 +3n/2). Find its nth term and the 20th term of this AP. arithmetic progression class-10 1 Answer +2 votes answered Sep 14, 2024 by AmirMustafa (60.4k points) selected Sep 23, 2024 by Vikash Kumar Best answer Hence, the 20th term is 99. ← Prev Question Next Question → Find MCQs & Mock Test
WebMar 3, 2024 · Given that Sum to n terms of an AP is . 3n² + n. Given common difference is 6, If suppose a is the first term of A.P and 'd' is the . common difference, the Sum to n terms of an A.P is. given by Sn = (n/2)*[2a + (n - 1)d] Given Sn = 3n² + n. If we substitute n = 1 , in Sn we get Sum to 1 tems of an A.P . which is equivalent to first term of A ... WebLet the sum of n terms be given by SnsoSn = 3n²/2+5n/2S1 = 3(1)²/2+5(1)/2= 3/2+5/2= 4So 1st term is 4 say aNowS2 = 3(2)²/2+5(2)/2= 6+5= 11Now a2 =S2−a1=> a2 =11−4= 7Now …
WebLet S n denotes the sum of first n terms of the AP. ∴ s n = 3n 2 + 5n. ⇒ `s_(n-1) = 3 (n-1) ^2 + 5 (n-1)` = `3(n^2 - 2n + 1) + 5 (n-1)` =`3n^2 -n-2` Now , n th term of AP , a n = s n - s n-1 = (3n 2 + 5n ) - ( 3n 2-n-2) = 6n + 2 . Let d be the common difference of the AP. ∴ d = a n - a n-1 = (6n + 2 ) - [ 6(n-1 ) +2] = 6n + 2 - 6 (n-1) -2 = 6 Web4 rows · 2 × Sum = n×(a+l) ⇒ Sum = n/2(a+l) Substituting the value of l in the previous equation, ...
WebIf the sum of the first n terms of an AP is 2n (n+3), then what is the series? first we will simplify the bracket 2n (n+3)=2n^2+6n If n=1 then 2*1^2+6*1=8 so our s1 is 8 If n=2 then 2*2^2+6*2=20 So our s2 is 20 if n=3 then 2*3^2+6*3=36 So our s3 is 36 then a1 is 8 a2 is s2-s1 that is 20–8=12 a3 is s3-s2 that is 36–20=16 so our ap is 8,12,16….
flynn chernosWebMar 27, 2024 · Solution For 10] Find the sum of first ' n ' terms of an AP 2 ,8 ,18 ,32 , 11] If α,β and γ are the zeroes of the polynomial P(x)=x3−6x2−x+30 then fin. The world’s only live instant tutoring platform. Become a tutor About us Student login Tutor login. Login. Student Tutor. Filo instant Ask button for chrome browser. ... greenough communications group incWebThe Sum of the First N Term Sofa an Ap is `( (3n^2) /2 +(5n) /2)`. Find Its Nth Term and the 25th Term . CBSE English Medium Class 10. Question Papers 939. Textbook Solutions 33590. MCQ Online Mock Tests 12. Important Solutions 4010. Question Bank Solutions 26519. Concept Notes & Videos 213. greenough coal merchantsWebMar 29, 2024 · Given Sn = 4n – n2 Taking n = 1 S1 = 4 × 1−12 = 4 – 1 = 3 ∴ Sum of first term of AP is 3 Taking n = 2 in Sn S2 = 4×2−2^2 S2 = 8 – 4 S2 = 4 ∴ Sum of first 2 terms is 4 But sum of first term will be the first term So, First term = a = 3 Finding 2nd term Sum of first 2 terms = 4 First term + Second term = 4 3 + a2 = 4 a2 = 4 – 3 a2 = 1 Hence, Common … greenough construction edmontonWebSep 15, 2024 · Solution: We can use our concept of AP here to solve the problem as follows: Step 1: Calculate the first number divisible by 3 in the given range: 20 = 3 × 6 + 2 a = 20 + (3 - remainder) a = 20 + (3 - 2) a = 21. Step 2: Calculate the Last number (nth) in the given range:-. flynn charges dismissedWebMar 30, 2024 · Given Sn = 2n2 + 3n Taking n = 1 S1 = 2 12 + 3 1 = 2 + 3 = 5 So, Sum of first term of AP is 5 But sum of first term will be the first term So, First term = a = 5 Taking n = … flynn chemicalWebMar 23, 2024 · The sum of the third and the seventh terms of an AP is 6 and their product is 8. Find the sum of first sixteen terms of the AP. 3. A ladder has rungs 25 cm apart. (see Fig. 5.7). The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. greenough consulting