Question

its answer is 36 i know but i need explanation some one help me correctly
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Answer 1

Answer:

sum of 3 terms =9

$\frac{n}{2} (2a + (n - 1)d) = 9 \\ \frac{3}{2} (2a + (3 - 1)d) = 9 \\ \frac{3}{2} (2a + 2d) = 9 \\ 3(a + d) = 9 \\1) a + d = 3$

sum of next three terms means that

sum of 6 terms =27

$\frac{6}{2} (2a + (6 - 1)d) = 27 \\ 3(2a + 5d) = 27 \\ 2a + 5d = 9$

by first equation

a=3-d

inserting in second equation

2(3-d)+5d=9

6-2d+5d=9

3d=3

d=1

a=3-1=2

$s10 = \frac{10}{2} (2(2) + (10 - 1)1) \\ = 5(4 + 9) \\ = 5 \times 13 \\ = 65$