You visited us 4 times! Enjoying our articles? Unlock Full Access!

Insertion of AM's Between 2 Numbers

Find the firs...

Question

Find the first term $a$ and the common difference $d$ of the arithmetic progression in which $a_{2} + a_{5} - a_{3} = 10$ , $a_{2} + a_{9} = 17$

Open in App

Solution

$a$ is the first term and $d$ is the common difference
$∵ a_{t} = a + (t - 1) d a_{2} + a_{5} - a_{3} = 10, ⟹ (a + d) + (a + 4 d) - (a + 2 d) = 10 ⟹ a + 3 d = 10 - - - - - - (i) a_{2} + a_{9} = 17 ⟹ a + d + a + 8 d = 17 ⟹ 2 a + 9 d = 17 - - - - - (i i) 2 \times (i) - (i i) ⟹ - 3 d = 3 ⟹ d = - 1$
Putting value in $(i i)$
$a - 3 = 10 ⟹ a = 13$
Answer, $a = 13$ & $d = - 1$

Suggest Corrections

Similar questions

A . P .

a_{2} + a_{5} - a_{3} = 10

a_{2} + a_{9} = 17,

a + d

a_{1}, a_{2}, a_{3}

a_{1} a_{3} + a_{2} a_{3}

a, a_{2}, a_{3}, . . . ., a_{n}

n

a = 0

d \neq 0

\frac{a_{3} - a_{2}}{a_{2}} + \frac{a_{4} - a_{2}}{a_{3}} + \frac{a_{5} - a_{2}}{a_{4}} . . . . + \frac{a_{n} - a_{2}}{a_{n - 1}}

a_{1}, a_{2}, a_{3}, . . . . . . . a_{n}

a_{1} = 0

d \neq 0

\frac{a_{3} - a_{2}}{a_{2}} + \frac{a_{4} - a_{2}}{a_{3}} + \frac{a_{5} - a_{2}}{a_{4}} . . . . . . . . . . . . \frac{a_{n} - a_{2}}{a_{n - 1}}

The n^th term (general term) of an arithmetic progression, a₁, a₂, a₃, …, a_n, … where a₂ –a₁ = a₃ – a₂ = …. = d is:

Join BYJU'S Learning Program