Question

If the sum of first 14 term of an
a.P is 1050 and its first term is 10, find the 20 th term. 0

Answer 1

The 20th term of the given AP is 200

Step-by-step explanation:

Step 1 :

Given,

The sum of the given AP's  first 14 terms    = 1050

The first term of the given AP = 10

We need to determine the 20th term

Step 2 :

The sum of  first n terms of any arithmetic progression=  $\frac{n}{2}$[2a + (n-1)d]

where a represents the first term, here a = 10

n is the number of terms

d represents  common difference

When n = 14 , the sum = 1050

Substituting this we have,

$\frac{14}{2}$ [ 2 × 10 + (14-1) d] = 1050

=> 20 + 13 d = 150

13 d = 130              

d = 10          

Step 3 :

The nth term of an AP  = a + (n-1) d

Here a = 10, n = 20 and d= 10

So the 20th term = 10 + (20-1) 10

                            = 10 + 19 × 10 = 200

Step 4 :

Answer :

The 20th term of the Arithmetic Progression is 200

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