WAEC Mathematics 2015 Theory — Question 14

Question 14 of 22 from the West African Examinations Council (WAEC) Mathematics 2015 Theory paper, with the correct answer and a full explanation.

9(a). The first term of an Arithmetic Progression (AP) is −8. If the ratio of the 7th term to the 9th term is 5:8, find the common difference of the AP.

Model answer

T_n = a+(n−1)d, with a=−8. T7=−8+6d, T9=−8+8d. Given T7:T9=5:8: (−8+6d)/(−8+8d)=5/8 → 8(−8+6d)=5(−8+8d) → −64+48d=−40+40d → 8d=24 → d=3.

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