Hits: 1838

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/13) | Q#4

Hits: 1838 Question Three geometric progressions, P, Q and R, are such that their sums to infinity are the first three  terms respectively of an arithmetic progression. Progression P is; Progression Q is; i.       Find the sum to infinity of progression R.    ii.       Given that the first term of R is 4, find the sum of the first three terms […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/12) | Q#8

Hits: 1618 Question a)   The sum, , of the first  terms of an arithmetic progression is given by . Find the  first term and the common difference. b)   A geometric progression in which all the terms are positive has sum to infinity 20. The sum of the  first two terms is 12.8. Find the first term of the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/11) | Q#7

Hits: 2848 Question i.       A geometric progression has first term , common ratio  and sum to infinity . A  second geometric progression has first term , common ratio  and sum to infinity . Find the  value of .    ii.       An arithmetic progression has first term 7. The nth term is 84 and the (3n)th term is 245. Find  the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/13) | Q#2

Hits: 839 Question The first term in a progression is 36 and the second term is 32.      i.       Given that the progression is geometric, find the sum to infinity.     ii.       Given instead that the progression is arithmetic, find the number of terms in the progression if  the sum of all the terms is 0. Solution i.   From the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/12) | Q#6

Hits: 985 Question The 1st, 2nd and 3rd terms of a geometric progression are the 1st , 9th and 21st terms respectively of  an arithmetic progression.  The 1st term of each progression is 8 and the common ratio of the geometric progression is r, where  r ≠ 1. Find     i.       the value of r,     ii.     the 4th […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/11) | Q#5

Hits: 916 Question An arithmetic progression has first term  and common difference . It is given that the sum of the first 200 terms is 4 times the sum of the first 100 terms.      i.       Find  in terms of .    ii.       Find the 100th term in terms of . Solution From the given information, we can compile […]