Question

Find the sum of the positive terms of the arithmetic sequence 85, 78, 71, ...​

Answer 1

$\huge \mathcal { \boxed{ \boxed{ \boxed {\red{ \blue{a \red{n} \blue{s} \red{w} \blue{e} \red{r}}}}}}} \:$

85, 78, 71,… is an A.P.

uₙ = a + (n-1) d

u₁ = a = 85

d = u₂ - u₁ = 78 - 85 = -7

Since we have to sum the positive terms,our terms must be greater than 0.

uₙ > 0

85 +(n-1) (-7) > 0

85 - 7n + 7 > 0

- 7n > - 92

7n < 92

n < 13.14

Thus, the first 13 terms are the positive terms.

Sₙ = n/2 {2a + (n-1)d}

S₁₃ = 13/2 {2(85) + 12(-7)}

S₁₃ = 13 { 85 -42 }

S₁₃ = 13 { 43 }

S₁₃ = 559