# The nth term of a sequence is given by an = 2n + 7. Show that it is an A.P. Also, find its 7th term.

Given,

an = 2n + 7

We can find first five terms of this sequence by putting values of n from 1 to 5.

When n = 1:

a1 = 2(1) + 7

a1 = 2 + 7

a1 = 9

When n = 2:

a2 = 2(2) + 7

a2 = 4 + 7

a2 = 11

When n = 3:

a3 = 2(3) + 7

a3 = 6 + 7

a3 = 13

When n = 4:

a4 = 2(4) + 7

a4 = 8 + 7

a4 = 15

When n = 5:

a5 = 2(5) + 7

a5 = 10 + 7

a5 = 17

First five terms of the sequence are 9, 11, 13, 15, 17.

A.P is known for Arithmetic Progression whose common difference = an – an-1 where n > 0

a1 = 9, a2 = 11, a3 = 13, a4 = 15, a5 = 17

Now, a2 – a1 = 11 – 9 = 2

a3 – a2 = 13 – 11 = 2

a4 – a3 = 15 – 13 = 2

a5 – a4 = 17 – 15 = 2

As, a2 – a1 = a3 – a2 = a4 – a3 = a5 – a4

The given sequence is A.P

Common difference, d = a2 – a1 = 2

To find the seventh term of A.P, firstly find an

We know, an = a + (n-1) d where a is first term or a1 and d is common difference

an = 3 + (n-1) 2

an = 3 + 2n – 2

an = 2n + 1

When n = 7:

a7 = 2(7) + 1

a7 = 14 + 1

a7 = 15

Hence, the 7th term of A.P. is 15

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