Find the first three terms of the arithmetic series. n = 18, an = 112, Sn = 1098?

Question

Find the first three terms of the arithmetic series. n = 18, an = 112, Sn = 1098?

1 Answer

Impact of this question

1355 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-08-08T14:20:26

$10, 16, 22$ $10,16,22$

Explanation:

$using the n th term and sum to n terms formulae$ $"using the n th term and sum to n terms formulae"$

$∙ x a_{n} = a_{1} + (n - 1) d$ $•color(white)(x)a_n=a_1+(n-1)d$

$∙ x S_{n} = \frac{n}{2} [2 a_{1} + (n - 1) d]$ $•color(white)(x)S_n=n/2[2a_1+(n-1)d]$

$given n = 18 then$ $"given "n=18" then"$

$a_{18} = a_{1} + 17 d = 112 \to (1)$ $a_(18)=a_1+17d=112to(1)$

$S_{18} = 9 [2 a_{1} + 17 d] = 1098$ $S_(18)=9[2a_1+17d]=1098$

$2 a_{1} + 17 d = \frac{1098}{9} = 122 \to (2)$ $2a_1+17d=1098/9=122to(2)$

$(2) - (1) \Rightarrow a_{1} = 10$ $(2)-(1)rArra_1=10$

$substitute a_{1} = 10 in equation (1)$ $"substitute "a_1=10" in equation "(1)$

$10 + 17 d = 112 \Rightarrow d = \frac{102}{17} = 6$ $10+17d=112rArrd=102/17=6$

$a_{1} = 10$ $a_1=10$

$a_{2} = a_{1} + d = 10 + 6 = 16$ $a_2=a_1+d=10+6=16$

$a_{3} = a_{2} + d = 16 + 6 = 22$ $a_3=a_2+d=16+6=22$

$the first 3 terms are 10, 16 and 22$ $"the first 3 terms are "10,16" and "22$

Science

Math

Humanities

... and beyond

Find the first three terms of the arithmetic series. n = 18, an = 112, Sn = 1098?

1 Answer

Explanation:

Related questions

Impact of this question