# Verify that the following is an AP, and then write its next three terms. a+b,(a+1)+b,(a+1)+(b+1),... - Mathematics

Sum

Verify that the following is an AP, and then write its next three terms.

a + b, (a + 1) + b, (a + 1) + (b + 1), ...

#### Solution

Here

a1 = a + b

a2 = (a + 1) + b

a3 = (a + 1) + (b + 1)

a2 – a1 = (a + 1) + b – (a + b) = 1

a3 – a2 = (a + 1) + (b + 1) – (a + 1) – b = 1

Since, difference of successive terms are equal,

Hence, a + b, (a + 1) + b, (a + 1) + (b + 1),… is an AP with common difference 1.

Therefore, the next three-term will be,

(a + 1) + (b + 1) + 1, (a + 1) + (b + 1) + 1(2), (a + 1) + (b + 1) + 1(3)

(a + 2) + (b + 1), (a + 2) + (b + 2), (a + 3) + (b + 2)

Concept: Arithmetic Progression
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#### APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 5 Arithematic Progressions
Exercise 5.3 | Q 2.(iv) | Page 52
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