Find an explicit formula for the arithmetic sequence 170,85,0,-85,......
d(n)=
Answers
Question :- Find an explicit formula for the arithmetic sequence 170,85,0,-85,...... T(n) = ?
Concept of Arithmetic Progression (AP) Series :-
• A sequence is said to be in AP (Arithmetic Progression), if the difference between its consecutive terms are equal.
• The nth term of an AP is given as ;
T(n) = a + (n-1)•d , where a is the first term and d is the common difference.
• The common difference of an AP is given as ;
d = T(n) - T(n-1)
• If the number of terms in an AP is n ( where n is odd ) ,then there will be a single middle term.
Also, [(n+1)/2]th term will be its middle term.
• If the number of terms in an AP is n ( where n is even ) ,then there will be two middle terms.
Also, (n/2)th and (n/2 + 1)th terms will be its middle terms.
• The sum up to nth terms of an AP is given as ;
S(n) = (n/2)•[2a + (n-1)•d] where a is the first term and d is the common difference.
• The nth term of an AP is also given as ;
T(n) = S(n) - S(n-1) .
Solution :-
Given AP series is :- 170,85,0,-85,......
So,
→ first term of AP = a = 170 = T(1)
→ second term of AP = 85 = T(2)
from above told concept , we have, The common difference of an AP is given as :-
→ d = T(n) - T(n-1)
→ d = T(2) - T(2 - 1)
→ d = T(2) - T(1)
→ d = 85 - 170
→ d = (-85).
Therefore,
The nth term of an AP is given as :-
→ T(n) = a + (n-1)•d , where a is the first term and d is the common difference.
Putting all values now , we get,
→ T(n) = 170 + (n - 1)(-85)
→ T(n) = 170 - 85n + 85
→ T(n) = 255 - 85n
→ T(n) = 85(3 - n) (Ans.)
Answer:
Cyclones and storm surges threaten coastal communities worldwide. The World Meteorological Organization defines a tropical cyclone as “a non-frontal synoptic scale cyclone originating over tropical or subtropical waters with organized convection and definite cyclonic surface wind circulation”.1More specifically, a storm in the south-east Indian Ocean is cyclonic when the sustained wind speed is more than 33 nautical miles per hour (> 62 km/h). The storm surge represents a major cause of death and injury during a cyclone. A storm surge is the difference between the water level under the influence of a disturbance (storm tide) and the normal level that would have been reached in the absence of the meteorological disturbance.2 Over the past two centuries, around two million people worldwide have died and millions have been injured as a result of tropical storms, including cyclones, hurricanes and typhoons.3 Globally, the number of cyclones has increased more than threefold (Fig. 1) from 1970 to 2006.4 The strength and number of major cyclones may be increasing because of higher sea surface temperatures associated with global warming.5Tropical cyclones and storm surges are particularly severe in the Bay of Bengal region.
Fig. 1. Frequency of cyclones in the world4

We review the impact of cyclones on health and livelihoods in Bangladesh, in light of the progress made and the challenges that remain. We explore cyclone-related severity and death in Bangladesh over the past 50 years, and discuss the experiences of other cyclone-afflicted countries. We also consider how we can learn from international experience to reduce the adverse health impacts of natural disasters. Finally, we recommend mitigation and adaptation strategies, and future research needs.
Cyclones in Bangladesh
Bangladesh is especially vulnerable to cyclones because of its location at the triangular shaped head of the Bay of Bengal,6 the sea-level geography of its coastal area, its high population density and the lack of coastal protection systems. During the pre-monsoon (April–May) or post-monsoon (October–November) seasons, cyclones frequently hit the coastal regions of Bangladesh. About 40% of the total global storm surges are recorded in Bangladesh,7 and the deadliest cyclones in the past 50 years, in terms of deaths and casualties, are those that have struck Bangladesh.8
The number and severity of cyclones in Bangladesh and the associated mortalities have varied greatly during the past 50 years (Table 1). The two deadliest cyclones occurred in 1970 and 1991, with > 500 000 and almost 140 000 deaths, respectively. However, during the past 20 years, Bangladesh has managed to reduce deaths and injuries from cyclones. For example, the most recent severe cyclone of 2007 caused 4234 deaths, a 100-fold reduction compared with the devastating 1970 cyclone.
Table 1. Cyclone severity and deaths in Bangladesh 1960–20109–11
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In addition to the immediate death and suffering caused by such disasters, cyclones also have direct and indirect impacts on general public health, livelihoods, infrastructure, the economy and sociocultural foundations. They can affect access to food and drinking water, and increase the transmission risks of infectious diseases, such as diarrhoea, hepatitis, malaria, dengue, pneumonia, eye infections and skin diseases,12 thus contributing to the interruption of livelihoods. Surface water, the main source of drinking water in coastal regions of Bangladesh, becomes contaminated by saline intrusion and poor sanitation systems.13,14 Open latrines and poor sanitation are common in rural Bangladesh and coastal areas, and cyclones make this situation worse.13 The lack of safe drinking water may be the most important cause of the spread of waterborne diseases after a cyclone. Other causes are through indirect impacts such as damaged infrastructure, population displacement, reduced food production and the release of contaminants into the water (e.g. from storage and waste disposal sites). Childhood malnutrition is already a serious issue in Bangladesh, and the loss of crops and reduced access to fish compounds the problem. Indirect health-related impacts, such as increased suicide and crime rates, and adverse pregnancy outcomes, are clearly associated with cyclones.15 These tend to increase in the post-disaster period, as a result of post-traumatic stress and depression. Literacy rates are low and poor knowledge of environmental health issues creates additional problems following a cyclone.
Progress and challenges