Question

If the third term of an Ap is 7 and 9th term is 19 find 27 th term

Answer 1

Solution is given in the above attachment..

Answer 2

Question:-

➡ If the third term of an AP is 7 and the 9th term is 19. Find the 27th term.

Answer:-

➡ The 27th term of the given AP is 55.

Step By Step Solution:-

• Let us assume that the first term of the given AP is a and Common Difference is d.

So,

3rd term = a+(3-1)d=a+2d

➡ a + 2d = 7 .....(i)

Again,

9th term = a+(9-1)d=a+8d

➡ a + 8d = 19 ......(ii)

Now, subtract equation (i) from (ii)

We get,

a + 8d - (a + 2d) = 19 - 7

➡ a + 8d - a - 2d = 12

➡ 6d = 12

➡ d = 12/6

➡ d = 2 (Keep it in mind)

Hence, the common difference, we get here is 2.

Now, putting the value of d in equation (i), we get,

a + 2×2 = 7

➡ a + 4 = 7

➡ a = 3 (Remember this)

Hence, the first

So,

27th term = a + (27-1)d

➡ 27th term = a + 26d

➡ 27th term = 3 + 26×2

➡ 27th term = 3+ 52

➡ 27th term = 55

Hence, the 27th term of the given AP is 55.

Formula Used:-

➡ Nth term of an AP = a + (n-1)d