Question

in an AP if a equals to -5 and common difference is 0 what will be the 100th term​

Answer 1

Answer :

Here, we are given the first term and the common difference of an arithmetic progression and we need to calculate the 100th term of A.P. So, for that we will use the following formula :

$\bf{t_n = a + (n - 1)d}$

where,

• a = First term of A.P.

• d = Common difference

• n = number of terms

Solution :

• Common difference of A.P. (d) = 0
• First term of A.P. (a) = - 5

To find :

• 100th term of A.P.

Solution :

$\\ \longrightarrow\bf{t_n = a + (n - 1)d}$

$\\ \longrightarrow\sf{t_{100} = - 5 + (100 - 1)0}$

$\\ \longrightarrow\sf{t_{100} = - 5 + (99)0}$

$\\ \longrightarrow\sf{t_{100} = - 5 + 99 \times 0}$

$\\ \longrightarrow\sf{t_{100} = - 5 + 0}$

$\\ \longrightarrow\sf{t_{100} = - 5 }$

Therefore,

• The 100th term of arithmetic progression = - 5

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Knowledge Bytes :

Some properties of A.P. :

• If a non - fixed zero number, i.e. number which is not equal to zero is subtracted or added to each term of the arithmetic progression then the resultant values are also an A.P.

• If a non - fixed zero number, i.e. number which is not equal to zero is divided or multiplied by all the terms of A.P. then the resultant values are also an A.P.