Question

how many terms are there in the a.p 7,10,13.....45 ​

Answer 1

Step-by-step explanation:

an=45

a=7

d=10-7= 3

n= ?

an=a+(n-1)d

45=7+(n-1)3

45=7+3n-3

45=4+3n

45-4=3n

41=3n

41/3= n

13.66=n

Answer 2

☯ Correct Question :

how many terms are there in the a.p 7, 10, 13.....43

$\rule{200}{2}$

★ Given :

• A.P : 7, 10, 13 ..... 43
• First term (a) = 7
• Common Difference (d) = 3
• Last term (An) = 43

★ To Find :

We have to find the number of terms (n) in the A.P

★ Explanation :

As, we have to find the number of terms (n) in the A.P. So, we can use the formula to calculate the last term of A.P. By using that formula we can calculate number of terms (n).

So,

$\large{\star{\underline{\boxed{\sf{A_n = a + (n - 1)d}}}}}$

$\sf{\dashrightarrow 43 = 7 + (n - 1)3} \\ \\ \sf{\dashrightarrow 43 = 7 + 3n - 3} \\ \\ \sf{\dashrightarrow 43 = 4 + 3n} \\ \\ \sf{\dashrightarrow 43 - 4 = 3n} \\ \\ \sf{\dashrightarrow 39 = 3n} \\ \\ \sf{\dashrightarrow n = \dfrac{\cancel{39}}{\cancel{3}}} \\ \\ \sf{\dashrightarrow n = 13} \\ \\ \Large{\star{\underline{\boxed{\sf{n = 13}}}}}$

$\rule{400}{4}$