Question

How many terms of the arithmetic progression $8,13,\mathrm{18....}$ add upto $645$?

• A. $14$
• B. $15$
• C. $16$
• D. $17$

Answer 1

The correct option is B $15$

$8+13+18+...+k=645$

No : of terms = ?

$S_n$ (Sum of AP) $=\frac{n}{2}(2a+(n-1\left)d\right)$

$645=\frac{n}{2}(2\times 8+(n-1\left)8\right)$

$(\because a=8;d=5S_n=645)$

$1290=n(16-5+5n)$

$5n^2+11n-1290=0$

$5n^2-75n+86n-1290=0$

$5n(n-15)+86(n-15)=0$

$(5n+86)(n-15)=0$

$n\ne \frac{86}{5}$ (cent be fraction)

$\therefore n=15$