Question

In an AP, the first term is 2, the last term is 29 and the sum of the term is 155, Find the sum of next 5 terms.​

Answer 1

Step-by-step explanation:

First term = 2

Last term (l) = 29

Sum of term = 155

Apply the Formula of Sum of Ap

$\bf\hugeS_{n} = \frac{n}{2} (a + l)$

$\bf\huge 155 = \frac{n}{2} (2 + 29)$

310 = 31n

$\bf\huge n = \frac{310}{31}$

n = 10

By the Information of Question

a10 = 29

a + 9d = 29

9d = 29 - 2

9d = 27

d = 27 / 9

Hence

d = 3

Now by applying sum formula you can find next terms

$\bf\huge S_{n} = \frac{n}{2}[2a + (n - 1)d]$

$\bf\huge S_{5} = \frac{5}{2}[2(2) + (5 - 1)3]$

$\bf\huge S_{5} = \frac{5}{2}[4 + 12]$

$\bf\huge S_{5} = \frac{5}{2}[16]$

= 40