Question

Find the sum of the first n terms of the arithmetic sequence.−9 + (−12) + (−15)+ ... (to 10 terms)

Polynomial arithmetic
ANSWERED
asked 2020-11-07

Find the sum of the first n terms of the arithmetic sequence.\(−9 + (−12) + (−15)+ ... \) (to 10 terms) Find the sum of the first 100 terms of an arithmetic sequence with 15th term of 86 and first term of 2.

Answers (1)

2020-11-08

Step 1 Given: \(-9 + (-12) + (-15)+....\) It is an arithmetic series with \(a = \text{first term} = -9\)
\(f = \text{common difference} = -12 - (-9) = -3\) Now sum of the first n terms is, \(S_n = \frac{n}{2} [2a + (n - 1)d]\)
\(\Rightarrow S_n = n/2 [2(-9) + (n - 1)(-3)]\)
\(\Rightarrow S_n = \frac{n}{2} [-18 - 3 n + 3]\)
\(\Rightarrow S_n = \frac{n}{2} [-15 - 3n]\)
\(\Rightarrow S_n = \frac{3n}{2} [5+n]\)

Step 2 Given \(a = 2\ and\ a_{15} = 86\) Consider, \(a_{15} = 86\)
\(\Rightarrow a+(15-1)d = 86 [ \because a_n=a+(n-1)d]\)
\(\Rightarrow 2+14d = 86\)
\(\Rightarrow 14d = 84\)
\(\Rightarrow d = 6\) Therefore the sum of the first 100 terms is, \(S_{100} = \frac{100}{2} [2(2) + (100 - 1)(6)] [ \because S_n = \frac{n}{2} [2a + (n - 1)d]]\)
\(= 50(4 + 594)\)
\(=29900\)

0
 
Best answer

expert advice

Need a better answer?

Relevant Questions

asked 2021-03-08

The general term of a sequence is given \(a_{n} = \left(\frac{1}{2}\right)^{n}\). Determine whether the sequence is arithmetic, geometric, or neither.
If the sequence is arithmetic, find the common difference, if it is geometric, find the common ratio.

asked 2020-11-30

The general term of a sequence is given \(a_{n} = 2^{n}\). Determine whether the sequence is arithmetic, geometric, or neither.
If the sequence is arithmetic, find the common difference, if it is geometric, find the common ratio.

asked 2021-02-09

Consider the following sequence. \(\displaystyle{s}_{{n}}={2}{n}−{1}\)

a) Find the first three terms of the sequence whose nth term is given.

\(\displaystyle{s}_{{1}}=\)

\({s}_{{2}}=\)

\({s}_{{3}}=\)

b) Classify the sequence as arithmetic, geometric, both, or neither. arithmeticgeometric bothneither If arithmetic, give d, if geometric, give r, if both, give d followed by r. (If both, enter your answers as a comma-separated list. If neither, enter NONE.)

asked 2020-12-29

a) Use base b = 10, precision k = 4, idealized, chopping floating-point arithmetic to show that fl(g(1.015)) is inaccurate, where \(\displaystyle{g{{\left({x}\right)}}}={\frac{{{x}^{{\frac{{1}}{{4}}}}-{1}}}{{{x}-{1}}}}\) b) Derive the second order (n = 2) quadratic Taylor polynomial approximation for \(f(x)=x^{\frac{1}{4}}\) expanded about a = 1, and use it to get an accurate approximation to g(x) in part (a). c) Verify that your approximation in (b) is more accurate.

...