Let a1, a2, ..., an be a given A.P.

Question

Let a1, a2, ..., an be a given A.P. whose
 common difference is an integer and
Sn = a1 + a2 + .... + an. If a1 = 1, an = 300 and 15 $$ \le $$ n $$ \le $$ 50, then
the ordered pair (Sn-4, an--4) is equal to:

Accepted Answer

${a_n} = {a_1} + (n - 1)d$

$$ \Rightarrow 300 = 1 + (n - 1)d$$

$$ \Rightarrow (n - 1)d = 299 = 13 \times 23$$

since, n $$ \in $$[15, 50]

$$ \therefore $$ n = 24 and d = 13

$${a_{n - 4}} = {a_{20}} = 1 + 19 \times 13 = 248$$

$$ \Rightarrow {a_{n - 4}} = 248$$

$${S_{n - 4}} = {{20} \over 2}\{ 1 + 248\}  = 2490$$

Solutions · 1