In an A.P., if first term is 4, 9th term is 20, then 15th term is

Answer (Detailed Solution Below)

Concept:

Let us consider sequence a1, a2, a3 . an is an A.P.

  • Common difference d= a2 a1 = a3 a2 = . = an an 1
  • nth term of the A.P. is given by an = a + (n 1) d
  • nth term from the last is given by an = l (n 1) d
  • sum of the first n terms = S = n/2[2a + (n 1) × d]

Or sum of the first n terms = n/2(a + l)

Where,

a = First term

d = Common difference

n = number of terms

an = nth term

l = Last term

Calculation:

Given:

1st term = 4 = a1

9th term = 20 = a9

We know, the formula for nth term of an A.P is

an = a1 + (n 1)d

a9 = a 1 + (9 1) d

a9 = a1 + (8) d

20 = 4 + 8d

16 = 8d

d = 2

Now,

a15 = a1 + (15 1) d

= a1 + (14) d

= 4 + 14 × 2

= 32

The 15th term of the A.P = 32

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