## find the sum of 5+8+11+-to10 terms using the formula​

Question

find the sum of 5+8+11+….to10 terms using the formula​

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2 weeks 2021-10-14T10:48:16+00:00 2 Answers 0 views 0

ns(n)t(n)1025=1,2,3,…=2+3n=5,8,11,…=∑k=1n2+3∑k=1nn=2n+3n(n+1)2=3n2+7n2=5,13,24,…=3n2+7n2⇒n=25

>>> [(n,2+3*n) for n in xrange(1,26)]

[(1, 5), (2, 8), (3, 11), (4, 14), (5, 17), (6, 20), (7, 23), (8, 26), (9, 29), (10, 32), (11, 35), (12, 38), (13, 41), (14, 44), (15, 47), (16, 50), (17, 53), (18,

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the series 5+8+11+….. can be written as 5+8+11+…+3n+2

the sum of the series can be written as S=5+8+11+…+3n+2. Also S=(3n+2)+(3n-1)+…+5. Therefore we can pair each number to each other such that each pair totals (3n+2)+5 or 3n+7. Therefore 2S=(3n+7) n times, that is n(3n+7) or 2S=n(3n+7)

2S=n(3n+7)

2S=3n²+7n since we want S =1025 2S=2050

2050=3n²+7n

3n²+7n-2050=0 then using using the quadratic formula for a=3, b=7, and c=-2050 we get n=(-7+/-157)/6. Since only the positive root will satisfy our question we take n=(-7+157)/6

n=25

the 25th term will be 3n+2 for n=25 . therefore the 25th term will be 3×25+2=77

Proof: S=(1/2)*n*(3n+7) set n=3 and solve to get S=1025

therefore there are 25 terms in the series when the total of the series is 1025.