Question

The first term of an arithmetic progression is -2222 and the common difference is 17. Find the value of the first positive term.

Answer 1

Sry for the cancellations
Hope it helps
:)

Answer 2

132th term is the first positive term and value of the first positive term is 5

Given :

The first term of an arithmetic progression is - 2222 and the common difference is 17

To find :

The value of the first positive term.

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 4 :

Write down first term and common difference

First term = a = - 2222

Common Difference = d = 17

Step 2 of 4 :

Find the nth term of the AP

The nth term

= a + (n - 1)d

= - 2222 + (n -1) × 17

= - 2222 + 17n - 17

= 17n - 2239

Step 3 of 4 :

Find the first positive term.

Let nth term of the AP is positive

∴ 17n - 2239 > 0

⇒ 17n > 2239

⇒ n > 2239/17

⇒ n > 131.71

Since n must be natural number

So the smallest value of n satisfying the above inequality is n = 132

So 132th term is the first positive term.

Step 4 of 4 :

Calculate value of the first positive term.

The value of the first positive term

= 132th term of the AP

= a + (132 - 1)d

= - 2222 + (131 × 17)

= - 2222 + 2227

= 5

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