Question

What term of the AP 2,5,8,.. is 56

Answer 1

Answer:

a=2,d=3,an=56

an=a+(n-1)d

2+(n-1)3=56

2+3n-3. =56

3n-1. =56

3n=57

n=19

The 19th term is 56

Answer 2

Given:

• An AP = 2,5,8,..,56

To Find:

• The value of the term gives us 56, (n).

Solution:

From the given AP we can say,

⇒a = 2 {first term}

⇒Second term = 5

⇒ Succesive difference, d = second term - first term = 5-2 = 3

⇒ The last term, $t_n$ = 56

We know for an AP,

$t_n$ = a+(n-1)d → {equation 1}

On substituting the values in equation 1 we get,

⇒ 56 = 2+(n-1)3 {removing the bracket by multiplying}

⇒ 56 = 2+3n-3 {subtracting like terms}

⇒ 56 = -1+3n

⇒ 3n = 56+1 {adding the terms}

⇒ 3n = 57

⇒ n = 57/3 = 19 {dividing the terms}

∴ The value of the term gives us 56, (n) = 19.