Question

9th term from the end of the AP 7,11,15,....... is 147 is

Answer 1

9th term from the last of the AP would be 115.

Given

• AP
• 7,11,15,....... is 147

To find

• 9th term from the end of the AP

Solution

we are provided with arithmetic progression and I asked to find the 9th term of the AP from its end.

This could be estimated directly by substituting the necessary values like the first term and common difference in the standard equation of the arithmetic progression that deals with the end terms directly.

the standard equation in this case would be,

an = l - (n-1)d

d = 11 -7

or, d = 4

where l represents the last term and n represents the term from end.

an = 147 - (9-1)×4

or, an = 147 - 8×4

or, an = 147 - 32

or, an = 115

Therefore, 9th term from the last of the AP would be 115.

Answer 2

Given :

an AP series :

7,11,15,....... is 147

To Find :

9th term from the end of AP series.

Step-by-step explanation:

first term : a = 7

last term : l = 147

term difference : d = 4

total no. of terms = n :

l = a + (n-1)d

147 = 7 + (n-1)(4)

(140/4) +1 = n

n = 36

9th term from the end :  

= (n - 9 +1 )th term from beginning

= (36-9+1)th from begining

= 28th term

= 7 + (28-1)(4)

= 115

Hence ;

9th term from the end of the AP = 115

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