Sir I want to take admission in the professional colleges in Andhra Pradesh so preparing for the APICET exam so can you please provide me some sequence and series problems for APICET

Hey buddy the APICET is the Integrated Common Entrance Test for admission in to MBA and MCA regular Courses offered by State Universities and Professional colleges in Andhra Pradesh

Sequence And Series Problems

Example:
At the end of each year the value of a certain machine has depreciated by 20% of its value at the beginning of that year. If its initial value was Rs 1250, find the value at the end of 5 years.
Solution:
After each year the value of the machine is 80% of its value the previous year (as it depreciates 20%) so at the end of 5 years the machine will depreciate by 5 times.
Hence, we have to find the 6th term of the G.P. whose first term a1 is 1250 and common ratio r is 0.8.Hence, the value at the end 5 years = T6 = a1r5 = 12.50 (0.8)5 = 409.6

Example:
The number of terms of the series 26,21,16,11... to be added so as to get the sum 74 is:
[1] 3
[2] 4
[3] 5
[4] 6
Solution:
In the given series: a= 26 and d = -5
Suppose sum of the first n terms is 74. This implies that —

Example:
The sums of the first ‘n’ terms of two arithmetic series are in the ratio(7n+1): (4n+27) . The ratio of their 11th terms is:
[1] 2:3
[2] 3:2
[3] 3:4
[4] 4:3

Solution:
It is given that
Therefore, using If Tn and T'n are nth the terms of two arithmetic progression and Sn and S'n are their sums of the first n terms, respectively then,

Substituting n = 11 in this equation we get

Example:
If the numbers 32a-1, 14, 34-2a (0<a<1) are the first three terms of an AP, then its fifth term is equal to
[1] 33
[2] 43
[3] 53
[4] 63
Solution:
The first three terms of the AP are: 32a-1, 14, 34-2a
Therefore, using a + c = 2b, where a, b, c are in AP, we have:

Substituting 9a = x , we get


This gives
9a = 81 or 9a = 3


Therefore, the numbers are 1,14,27 which are in AP with common difference 13.
Therefore, the fifth term is 1 + 4 x 13 = 53.