Question

the 10th term of An ap 3,7, 11.... is -----​

Answer 1

Answer :

Explanation :

Given :

• Series : 3,7,11,...

To find :

• 10th term of the AP.

Knowledge required :

Formula for common difference :

⠀⠀⠀⠀⠀⠀⠀⠀⠀d = an - a(n - 1)

Where,

• d = Common Difference
• a = Any term of the AP

Formula for nth term of an AP :

⠀⠀⠀⠀⠀⠀⠀⠀⠀tn = a1 + (n - 1)d

Where,

• tn = nth term of the AP
• n = no. of terms
• d = Common Difference
• a1 = First term

Solution :

First let us find the common difference of the AP :

By using the formula for common difference and substituting the values in it, we get :

⠀⠀⠀⠀=> d = an - a(n - 1)

⠀⠀⠀⠀=> d = a(3) - a(2)

⠀⠀⠀⠀=> d = 11 - 7

⠀⠀⠀⠀=> d = 4

⠀⠀⠀⠀⠀⠀⠀⠀⠀∴ d = 4

Hence the common difference of the AP is 4

To find the 10th term of the AP :

By using the formula for nth term of the AP and substituting the values in it, we get :

⠀⠀⠀⠀=> tn = a1 + (n - 1)d

⠀⠀⠀⠀=> t(10) = 3 + (10 - 1) × 4

⠀⠀⠀⠀=> t(10) = 3 + 9 × 4

⠀⠀⠀⠀=> t(10) = 3 + 36

⠀⠀⠀⠀=> t(10) = 39

⠀⠀⠀⠀⠀⠀⠀⠀⠀∴ t(10) = 39

Hence the 10th term of the AP is 39.

Answer 2

Given:-

• A.P. = 3,7,11

Find:-

• $\sf 10^{th}$ term of the A.P.

Solution:-

Here,

⇰a = 3

⇰d = a₂ - a₁ = 7 - 3 = 4

Now, we know that

➠ a(n) = a + (n - 1)d

where,

• a = 3
• d = 4
• n = 10

◕ Substituting these values ◕

➺ a(n) = a + (n - 1)d

➺ a(10) = 3 + (10 - 1)4

➺ a(10) = 3 + (9)4

➺ a(10) = 3 + 36

➺ a(10) = 39

So, the 10th term of the given A.P. is 39