If the sum and product of the first three terms in an A.P.

Question

If the sum and product of the first three terms in an A.P. are $33$ and $1155$, respectively, then a value of its 11th term is:

Accepted Answer

Let the three terms are a - d, a, a + d

Given a - d + a + a + d = 33

$$ \Rightarrow $$ 3a = 33

$$ \Rightarrow $$ a = 11

Also given,

(a - d)a(a + d) = 1155

$$ \Rightarrow $$ (a2 - d2)a = 1155

$$ \Rightarrow $$ (112 - d2)11 = 1155

$$ \Rightarrow $$ (112 - d2) = 105

$$ \Rightarrow $$ d = $$ \pm $$ 4

When d = 4 and a = 11 then series is

7, 11, 15, ....

$$ \therefore $$ T11 = a + 10d = 7 + 10$$ \times $$ 4 = 47

When d = -4 and a = 11 then series is

15, 11, 7, ....

$$ \therefore $$ T11 = a + 10d = 15 + 10$$ \times $$ -4 = -25

Solutions · 1