Question

Find wether 55 is a term of A. P :7,10,13,....,...,or not (plz full explain) ​

Answer 1

Given :

AP series

7 , 10 , 13 , ...

To Find :

Whether 55 is the term of an given AP

Solution :

nth of an AP is given by ,

$\sf \bigstar\ \; a_n=a+(n-1)d$

where

• a denotes first term
• n denotes number of terms
• d denotes common difference

Given ,

• aₙ = 55
• a = 7
• d = 10 - 7 = 3

$\to \sf a_n=a+(n-1)d\\\\\to \sf 55=7+(n-1)3\\\\\to \sf 55=7+3n-3\\\\\to \sf 55=4+3n\\\\\to \sf 3n=51\\\\\to \sf n=17\ \; \bigstar$

So , 17th term of an AP is 55

Answer 2

Answer:

Step-by-step explanation:

The given term is part of the A.P only when the 'x' calculated by substituting the values is a positive number.

Here,

a = 7

d = 10 - 7 = 3

Let aₓ = 55.

We know,

aₓ = a + (x - 1)d

55 = 7 + (x - 1)3

48 = (x - 1)3

x - 1 = 16

x = 17, which is a natural number.

Thus, 55 is a term of the A.P.

If you find any mistake in the solution, please list it in the comments :)