Sequences & Series
Finite series summation
nta_pyq_2025_apr
Grade 12
Question:
If the sum of the first 20 terms of the series 4.1 4.2 4.3 4.4 + + + +$\ldots 2 4 2 4 2 4 2 4$4+3.1 +1$$4+3.2 +2$$4+3.3 +3$$$$4+3.4 +4$is m n, where m and n are coprime, then$m + n$is equal to$:-
Step-by-Step Solution
Key Concept: Decompose the finite series into standard sums over$n$and evaluate for$20$terms.
20 4r$\sum$(3)$$r=1$$4 + 3r$$2 + r$4 20 4r$$$\sum 2 2 ($$r + r + 2)$($r - r + 2)$$r=1$20 1 1 2$$\sum( - ) 2 2$r - r + 2$$r + r + 2$$r=1$1 1 2( - ) 2 4 1$1 - 4$8 1$1 - 8$14 1 1 ( - ) 382 422 1$1 = 2( - )$2 422$420 = 422$$210 = 211$option (3)$
Correct Answer: 3