Sequences & Series
GP term sums
nta_pyq_2025_apr
Grade 12
Question:
If the sum of the second, fourth and sixth terms of a G.P. of positive terms is 21 and the sum of its eighth, tenth and twelfth terms is 15309, then the sum of its first nine terms is:
Step-by-Step Solution
Key Concept: Use GP term formulas to express the sums of second, fourth, sixth and eighth, tenth terms in powers of$r^2$.
3 5 7 9 11$ar + ar + ar = 21$,$ar + ar + ar = 15309$2 4 7 2 4$(4)$$\Rightarrow$ ar($1 + r + r$) = 21, ar ($1 + r + r$) = 15309$(2)$¯ ¯¯¯¯ n n Eq$(2)$$\div$ eq$(1)$$(2)$$(1)$7 a$\cdot r 15309 6$$\Rightarrow$ = $\Rightarrow$$r = 729$ar 21 7 9 a$\cdot ($r - 1)$($19683 - 1)$91 7$$\times$ 19682 $\Rightarrow$ = =$r - 1$2 91 $\times$ 2 9841 = = 757 13
Correct Answer: 4