Question

The 21st term of AP whose first two teams are
-I and 2 is
(a) 61
(b)59
(c)43
(d) 57​

Answer 1

Given :

• First term $a_{1}$ = -1

• Second term $a_{2}$ = 2

To find :

The 21st term of the AP.

Solution :

To find the 21st term of the AP first we need to find the Common Difference of the AP.

We know the formula for Common Difference ,i.e,

$\underline{:\implies \bf{d = a_{n} - a_{n - 1}}}$

Where :-

• d = Common Difference
• a = Term of the AP

Using the above formula and substituting the values in it , we get :-

$:\implies \bf{d = a_{n} - a_{n - 1}}$

$:\implies \bf{d = 2 - (-1)}$

$:\implies \bf{d = 2 + 1}$

$:\implies \bf{d = 3}$

Hence , the common difference of the AP is 3.

⠀⠀⠀⠀⠀⠀⠀21st term of the AP —

Now , using the formula and substituting the values in it , we get :-

$\underline{:\implies \bf{t_{n} = a_{1} + (n - 1)d}}$

Where :-

• $t_{n}$ = nth term
• $a_{1}$ = First term
• n = No. of terms
• d = Common Difference

Here ,

• d = 3
• n = 21
• $a_{1}$ = -1

Using the formula and substituting the values in it , we get :-

$:\implies \bf{t_{n} = a_{1} + (n - 1)d}$

$:\implies \bf{t_{n} = -1 + (21 - 1) \times 3}$

$:\implies \bf{t_{n} = -1 + 20 \times 3}$

$:\implies \bf{t_{n} = -1 + 60}$

$:\implies \bf{t_{n} = 59}$

$\underline{\therefore \bf{t_{n} = 59}}$

Hence, the 21st term of the AP is 59.