Question

find next two terms of a.p whose first term and common difference are the same and sum of both is 6​

Answer 1

GIVEN:

• First term and common difference of an AP are same
• Sum of common difference and first term is 6.

TO FIND:

• What are the next two terms of an AP ?

SOLUTION:

Let 'a' be the first term and 'd' be the common difference of an AP

We have given that,

• a = d

✏ In this case, sum of common difference and first term is 6.

According to question:-

➸ a + d = 6

➸ 2a = 6 [∴ a = d]

➸ a = $\sf{\cancel\dfrac{6}{2}}$

❮ a = 3 ❯

• a = d = 3

Next two terms of an AP are:-

➸ a + d = 3 + 3 = 6

➸ a + 2d = 3 + 2(3) = 9

❝ Hence, the next two terms of an AP are 6 and 9 ❞

______________________

Answer 2

Given ,

• The first term and common difference of AP is same

• The sum of first term and common difference is 6

According to the question ,

a + d = 6

a + a = 6 { beacuse , d = a }

2a = 6

a = 6/2

a = 3

$\therefore$ The first term and common difference of AP are 3 and 3

Now , the next two terms of AP will be

• a + d = 6
• a + 2d = 9