Question

Which term of the A.P. 4, 9, 14, ... is 89? Also, find the sum 4 + 9 + 14 + + 89.

Answer 1

Answer:

19 ans.

Step-by-step explanation:

Answer 2

$\huge\sf\pink{Answer}$

☞ n = 18

☞ Sum = 837

$\rule{110}1$

$\huge\sf\blue{Given}$

✭ A.P. 4, 9, 14, ... is 89

$\rule{110}1$

$\huge\sf\gray{To \:Find\;To\;Prove}$

❍ The sum of the A.P?

$\rule{110}1$

$\huge\sf\purple{Steps}$

Here,

a = 4

d = (9 - 4) = 5

l = 89

Let the total number of terms be n. Then,

Tₙ = 89

➝ a + (n - 1)d = 89

➝ 4 + (n - 1) * 5 = 89

➝ 4 + 5n - 5 = 89

➝ 5n - 1 = 89

➝ 5n = 89 + 1

➝ 5n = 90

➝ n = $\sf \dfrac{90}{5}$

➝ $\sf\green{ n = 18}$

Required sum = $\sf\dfrac{n}{2} \:. \: (a + l)$

➳ Sum = $\sf \dfrac{18}{2} \:. \: ( 4+ 89)$

➳ Sum = 9 × 93

➳ $\sf\orange{ Sum = 837}$

$\rule{170}3$