Sequence and Series

1. The 1st term of an arithmetic sequence is 1 and the 9th term is 15. Calculate the middle term and T 2. If 5 and 40 are the second and last terms of a geometric progression, find the sum of the first four terms if there are seven terms in the geometric progression. 3. A shrub of height 110 cm is planted. At the end of the first year the shrub is 125 cm tall. Thereafter the growth of the shrub each year is third of its growth in the previous year. Show that the height of the shrub will never exceed 132,5 cm. 31 21 174. The sum of the 4th and the 9th terms of an arithmetic sequence is 0. If the sum of the first 6 terms is 36, determine the 7th term. 5. Sn = 4n + 2 represents the sum of the first n terms of a particular series. Determine the value of the 9th term. 8 6. Calculate: Σ . k = 3 2 2 ) 21 ( 16  k7. The sequence x; is given. Determine the value of x if the sequence is 7.1 arithmetic. 7.2 geometric. 8. Consider the geometric sequence: 16(x – 2) ; 8(x – 2) ; 4(x – 2) ; x ≠ 2 8.1 Determine the value of x for which the sequence converges. 8.2 Determine the sum to infinity of the series if x = 2,5. 31 41 4 16 2 3 49. Calculate the value of n, the number of terms, in the equation: nΣ (2p-3)=240 p=1 2