CBSEi Class 10 Sequences (AP and GP) CORE

ealise that if general term is given they can write the specified terms without
writing all terms in continuation. For example if general term tn = 5n+6, it is possible
to write 100 th term by substituting n= 100 in tn.
Further the students can be asked to observe the similarities between the following
sequences:
2, 4, 6, 8.....
4, 7, 10....
11, 16, 21.......
Let them come out with the observation that in each case the difference between the
consecutive terms is same. For such sequence there is special name i.e. Arithmetic
sequence. Emphasis is to be laid on building the vocabulary of this unit as all the
terms are new for the students – first term, common difference, arithmetic sequence,
arithmetic progression etc.. In the same way geometric progression and related
terms can be introduced.
Teacher should take care that learner is able to use the vocabulary and symbols
carefully as this chapter also laid the foundation for functions. They shall further be
encouraged to explore that terms of all arithmetic progressions observe linear
relation and geometric progression observe exponential relation. By observing the
pattern in numbers students shall be able to get the general term as an=a+(n-1)d for
A.P. and an=ar n-1 for G.P.
Sum of first n terms can be introduced using GAUSS METHOD. Following incident
from life of Gauss can be shared to motivate them-
One day teacher of Gauss gave a problem to the students in order to engage them for
a long time. Problem was to find the sum of first 100 numbers. Gauss got the
solution in 20 seconds and surprised his teacher. What was the method?
He Wrote (1+2+3+.....................+100)
(100+99+98+..................+1) = 101 x 100 = 10100
101+101+...................+101
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