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Arithmetic Progressions

Question
CBSEENMA10008067
Wired Faculty App

Find the sum of the series :

4 + 8 + 12 +......... + 100.

Solution
Let ‘b’ be the first term and ‘d’ the common difference of the A .P.
a = 4, d = 4,  an = 100 =  1
We know that,  an = a+ (n -1)d
rightwards double arrow   100 = 4 + (n - 1) d
rightwards double arrow   100 = 4 + (n - 1) 4
rightwards double arrow    4n = 100
rightwards double arrow    n = 25
And comma space space straight S subscript straight n equals straight n over 2 left square bracket straight a plus straight l right square bracket space space space left square bracket because space straight l space equals straight T subscript straight n right parenthesis right square bracket So comma space space space space straight S subscript 25 equals 25 over 2 space space space left square bracket 4 space plus space 100 right square bracket space space space space space space space space space space space space space space equals 25 over 2 cross times 104 equals 25 cross times 52 space space space space space space space space space space space space space space space equals space 1300

Some More Questions From Arithmetic Progressions Chapter

Write first four terms of the AP, when the first term a and the common difference d are given as follows:
a = –2, d = 0

Write first four terms of the AP, when the first term a and the common difference d are given as follows:
a = 4, d = – 3

Write first four terms of the AP, when the first term a and the common difference d are given as follows:

a = – 1.25, d = – 0.25

For the following APs, write the first term and the common difference
3, 1, – 1, – 3, . . .

For the following APs, write the first term and the common difference
– 5, – 1, 3, 7, . . .

For the following APs, write the first term and the common difference
0.6, 1.7, 2.8, 3.9, . . .

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