Question

what is value of t25 and t5 for A.P 9,14,19.... give explinetion ​

Answer 1

SOLUTION

Given :- AP = 9,14,19...

Here ,

First Term (t) = 9

Common Difference (d) = a₂ - a₁ = 14 - 9 = 5

$\boxed{\red\sf t= 9 \: and \:d = 5}$

We are asked to find the value of  t25 and t5 of the  A.P

We know the formula of tn of an AP

$\boxed{\sf tn = t + (n - 1)d }$

Here n = 25 and n = 5

Let us find t₂₅ of the AP

t₂₅ = 9 + ( 25 - 1 ) 5

t₂₅ = 9 + 24 × 5

t₂₅ = 9 + 120 = 129

Now Let us find t₅ of the AP

t₅ = 9 + ( 5 - 1 )5

t₅ = 9 + 4 × 5

t₅ = 9 + 20 = 29

$\red\bigstar$ t₂₅ of the AP = 129 and t₅ of the AP = 29