Question

for an A.P first two term are -3'4 Then 21st term is .....

Answer 1

The sum of first m terms of an A.p. is 4m2-m. If its nth term is 107, find the value of n. Also find the 21st term of this A.p

Answer 2

Answer:

the 21st term is 137.

Step-by-step explanation:

An arithmetic sequence is given by:

$a_1, a_2, a_3,....., a_n,.....$

The nth term for this sequence is :

$a_n = a_1+(n-1)d$

where,

$a_1$ is the first term

d is the common difference of two consecutive terms

n is the number of terms.

Given the statement:

An A.P first two terms are -3 and 4

⇒$a_1 = -3$ and $a_2 = 4$

Using nth term:

For n=2

$a_2 = a_1 +(2-1)d$

⇒$a_2 = -3+d$

⇒$4 = -3+d$

Add 3 to both sides we have;

$d = 7$

We have to find the 21st term:

for n= 21

we have;

$a_{21} = a_1 +(21-1)d$

⇒$a_{21} = -3+20d$

⇒$a_{21} = -3+20(7) = -3+140 = 137$

Therefore, the 21st term is 137.