Question

The 21st term of an AP whose first two terms are -3 and 4 is (a) 17,(b) 137,(c) 143,(d) -143​

Answer 1

21st term of the AP = 137

Given :

The first two terms are - 3 and 4

To find :

The 21st term of an AP whose first two terms are - 3 and 4 is

(a) 17

(b) 137

(c) 143

(d) - 143

Concept :

If in an arithmetic progression

First term = a

Common difference = d

Then nth term of the AP

= a + ( n - 1 )d

Solution :

Step 1 of 3 :

Write down the given data

Here it is given that first two terms of the AP are - 3 and 4

Step 2 of 3 :

Write down first term and common difference

First term = a = - 3

Second Term = 4

We know that for a given arithmetic progression Common difference is the difference between two consecutive terms in the arithmetic progression

Common Difference

= d

= 4 - ( - 3)

= 4 + 3

= 7

Step 3 of 3 :

Find 21st term of the AP

21st term of the AP

$\sf = a_{21}$

= a + ( 21 - 1 )d

= a + 20d

= - 3 + [ 20 × 7 ]

= - 3 + 140

= 137

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Answer 2

Answer:

The 21st term of an AP whose first two terms are -3 and 4 is 137.

Step-by-step explanation:

As per the data given in the questions,

We have,

first term (a1) = -3

second term (a2) = 4

$difference (d) = 4-(-3)$

d=7

As we know,

$nth\:term = a1 + (n-1)d$

$21st\:term = (-3) +(21-1)\times 7$

$= -3 + (20)\times7$

$= 140-3$

$=137$

∴The 21st term of an AP whose first two terms are -3 and 4 is 137.

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