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RV-22-001 · Sequence: consecutive terms and a limiting condition

The nth term of a sequence is 6n+146n + 14.

(a) Two consecutive terms have sum 430. Find the positions of these terms.

(b) Find the position of the last term not exceeding 241.

Part (a) Sequences: Consecutive Terms Equation & Inequality Bound Booklet p. 10, p. 15 & p. 25
Method
1) Add nth term and (n+1)th term, set equal to sum, and kill, kill to find n
2) Solve an + b ≤ limit and take greatest integer n
Worked Example (RV-22-001 · Part (a))
Two consecutive terms have sum 430. Find the positions of these terms.
1)
6n+146n + 14 + 6(n+1)+146(n+1)+14 = 430.
2)
Simplify and solve the linear equation.
3)
Positions 33 and 34.
Ans = 33 and 34.
Part (b) Sequences: Consecutive Terms Equation & Inequality Bound Booklet p. 10, p. 15 & p. 25
Method
1) Add nth term and (n+1)th term, set equal to sum, and kill, kill to find n
2) Solve an + b ≤ limit and take greatest integer n
Worked Example (RV-22-001 · Part (b))
Find the position of the last term not exceeding 241.
1)
6n+14≤2416n + 14\le 241
2)
n = 37; use the greatest admissible integer.
Ans = 37