The second term of a geometric progression is 16 and the sum to infinity is 100.

Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

1. [B1] ar = 16, a/(1-r) = 100 leading to a = 16/r and a = 100(1-r) Rearranging two algebraic statements to give a =. These can be implied by a correct equation in one variable.
2. [*M1] 100(1-r)r=16 leading to 100r² -100r+16[=0] Using their two expressions and rearranging to get a 3-term quadratic expression with all of the terms on one side. Condone sign errors only.
3. [DM1] (5r-4)(5r-1) = 0 Condone (5r-4)(5r-1) following 100r² – 100r +16.
4. [A1] a = 20, a = 80 SC: if DM0 scored SCB1 is available for sight of 20 and 80.
5. [B1] r = 4/5, 1/5 SOI 2 expressions for the nth term FT their values from part (a) if |r| less than 1.
6. [B1FT] [u_n =] their 20 × their (4/5)^(n-1) [v_n =] their 80 × their (1/5)^(n-1)
7. [M1] Correctly separating the numerator and denominator of their (4/5)^(n-1) or one correct step towards the solution eg u_n = 80 × 4^(n-2) / 5^(n-1).
8. [A1] 4^(n-2) × v_n AG Given result clearly shown