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Arithmetic Progressions

Question
CBSEENMA10008078
Wired Faculty App

Find the sum of the series :
–5 + (–8) + (–11) +........ + (–230).

Solution
Let ‘a’ be the first term and d the common difference then,
a = - 5,  d = - 3, an = - 230 = l
We know that, an = a + (n - 1) d
rightwards double arrow -230 = - 5 + (n - 1) ( - 3)
rightwards double arrow - 230 = -5 - 3n + 3
rightwards double arrow - 230 = -2 - 3n
rightwards double arrow - 228 = -3n
rightwards double arrow space space straight n space equals space 228 over 3 equals 76
We space know space that comma space straight S subscript straight n equals straight n over 2 left square bracket straight a plus straight l right square bracket So comma space space space straight S subscript 16 equals 76 over 2 left square bracket negative 5 space plus space left parenthesis negative 230 right parenthesis right square bracket space space space space space space space space space space space space space equals space 38 space left parenthesis negative 235 right parenthesis space minus 8930.

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 = 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, . . .

Which of the following are APs ? If they form an AP, find the common difference d and write three more terms.
– 1.2, – 3.2, – 5.2, – 7.2, . . .

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