CBSE Class 10 Maths (Basic) 2022 · Paper 430/6/1 · Question 4

Arithmetic Progressions 2 marks Medium

The

n^{th}

term of a sequence is given by

a_{n} = \frac{n ( n + 1 ) ( 2 n + 1 )}{6}

. Write the first three terms of the sequence. Does this sequence form an A.P. ? Justify your answer.

Answer

First three terms:

1, 5, 14

. The sequence is **not** an A.P. Because

a_{2} - a_{1} = 4

while

a_{3} - a_{2} = 9

, so the common difference is not constant.

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