Question

How many terms are there in AP . 7,10,13,...43?

Answer 1

✬ Terms = 13 ✬

Step-by-step explanation:

Given:

• Given AP series is 7 ,10 , 13....43.

To Find:

• How many terms are there in AP?

Solution: Let number of terms be n. Here in this AP series we have

➟ First term is a = 7

➟ Common difference is d = 10 – 7 = 3

➟ Last term is 43.

As we know that an AP series is given by

★ aⁿ = a + (n – 1)d ★

$\implies{\rm }$ 43 = 7 + (n – 1)3

$\implies{\rm }$ 43 = 7 + (3n – 3)

$\implies{\rm }$ 43 = 7 + 3n – 3

$\implies{\rm }$ 43 = 4 + 3n

$\implies{\rm }$ 43 – 4 = 3n

$\implies{\rm }$ 39 = 3n

$\implies{\rm }$ 39/3 = n

$\implies{\rm }$ 13 = n

Hence, number of terms in AP is 13.

Answer 2

Answer:

let n be the total term in AP.

here, a=7,d=10-7=3,l=43

43=7+(n-1)3

43-7=3(n-1)

36=3(n-1)

n-1=36/3

n-1=12

n=12+1=13

so, total no of term is 13.

hope it will help you