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Question -

For the A.P.: -3, -7, -11,…, can we find a30 – a20 without actually finding a30 and a20 ? Give reasons for your answer. [NCERT Exemplar]



Answer -

True.
nth term of an A.P., an = a + (n – 1)d
a30 = a + (30 – 1 )d = a + 29d
and a20 = a + (20 – 1 )d = a + 19d …(i)
Now, a30 – a20 = (a + 29d) – (a + 19d) = 10d
and from given A.P.
common difference, d = -7 – (-3) = -7 + 3 = -4
a30 – a20 = 10(-4) = -40 [from Eq- (i)]

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