Question

Which term of the AP 3,7,11,15,.... is 79. Also find the sum 3+7+11+....+79

Answer 1

Solution is attached below

Answer 2

The 20th term is 79 and the sum = 820.

Step-by-step explanation:

Let us assume that 79 is the nth term of the A.P.

Now, the A.P. is given by 3, 7, 11, 15, ........

So, the series has the first term (a), 3 and the common difference (d), 4.

So, the nth term = a + (n - 1)d = 79

⇒ 3 + (n - 1)4 = 79

⇒ n - 1 = 19

⇒ n = 20

So,the 20th term of the A.P. is 79.

Now, Sum of an A.P. up to the nth term is given by $S_{n} = \frac{n}{2}[2a + (n - 1)d]$

So, 3 + 7 + 11 + ...... + 79

= $\frac{20}{2}[2\times 3 + (20 - 1) \times 4]$

= 820 (Answer)