Question

An A.P. consists of 50 terns, in which 3rd term is 12 and the last term os 106. Find 29th term.

Please I need the answer urgently.​

Answer 1

Given:-

• An A.P. consists of 50 terms.
• 3rd term is 12.
• Last term is 50.

To find:-

• 29th term.

Solution:-

We know,

an = a + (n - 1 ) × d

Therefore,

= a3 = a + (3 - 1) × d

=> 12 = a + 2d

=> a + 2d = 12 ----------> (i)

Again,

= a50 = a + (50 - 1) × d

=> 106 = a + 49d

=> a + 49d = 106 --------> (ii)

Subtracting eq. (i) from eq. (ii)

= (a + 49d = 106) - (a + 2d = 12)

a + 49d = 106

- a - 2d = -12

= 47d = 94

=> d = 94/47

=> d = 2

Putting the value of d in eq. (i)

a + 2d = 12

=> a + 2×2 = 12

=> a + 4 = 12

=> a = 12 - 4

=> a = 8

Now,

To find 29th term,

a29 = 8 + (29 - 1) × 2

= 8 + 28 × 2

= 8 + 56

= 64 $\red{\boxed{\sf\red{Answer}}}$

Therefore the 29th term is 64.