Question

if 7th and 13th terms of an A.P be 34 and 64 respectively, then its 18th term is

Answer 1

T7 = 34
=> a+6d = 34------(1)

T13 = 64
=> a+12d = 64 ------(2)

On subtracting equation 1 from 2, we get
6d = 30
=> d = 5

a = 4

T18 = a+17d
= 4+ 17*5
= 4+85
= 89

Answer 2

If 7th and 13th term of an AP be 34 and 64 respectively , then its 18th term is 89

Given :

7th and 13th term of an AP be 34 and 64 respectively

To find :

The 18th term of the AP

Concept :

If in an arithmetic progression

First term = a

Common difference = d

Then nth term of the AP

= a + (n - 1)d

Solution :

Step 1 of 3 :

Form the equation to find the term

Let first term = a and common difference = d

Then we have ,

7th term = a + (7 - 1)d = a + 6d

13th term = a + (13 - 1)d = a + 12d

Now it is given that the 7th and 13th term of an AP be 34 and 64 respectively

By the given condition

a + 6d = 34 - - - - - (1)

a + 12d = 64 - - - - - (2)

Step 2 of 3 :

Find the common difference

a + 6d = 34 - - - - - (1)

a + 12d = 64 - - - - - (2)

Equation 2 - Equation 1 gives

6d = 30

⇒ d = 30/6

⇒ d = 5

Step 3 of 3 :

Find 18th term of the AP

18th term of the AP

= a + (18 - 1)d

= a + 17d

= a + 6d + 11d

= (a + 6d) + 11d

= 34 + (11 × 5)

= 34 + 55

= 89

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ 2,7,12,17,...sum of 12 terms of this A. P. is

https://brainly.in/question/24134044

2. find the 100th term of an AP whose nth term is 3n+1

https://brainly.in/question/22293445

#SPJ3