Question

in an ap the common difference d,the seventh term a7(154) than find the first term

Answer 1

Let first term is a and common difference d
A/C to question,
7th term = a₇ = 154
We know, one thing aₓ = a + (x - 1)d , by formula of nth term
So, a₇ = a + (7 - 1)d = 154
a + 6d = 154
a = 154 - 6d

Hence, first term is (154 - 6d)

Answer 2

Hey there!

A collection of numbers following a certain rule by which any term can be find out ,then such a collection is called Series.

Arithmetic progression is a series of numbers which have a common difference between the consecutive numbers.

If a is the first term of any A. P, and b, c, d are it's consecutive terms

then , d - c = c - b = b - a = d [ Common difference ]

Also, the n th term of A. P = a + ( n-1)d .

Sum of n terms = n/2 [ 2a + (n-1) d ]

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In the given problem :

Common difference = d.

Seventh term = 154 .

Let the first term be " a "

$given \\ a_{7} = 154 \\ we \: know \: that \: \: \\ \\ a_{m } = a + (m - 1)d \\ \\ now \: \\ a_{7} = a + (7 - 1)d \\ \: \: \: \: \: = a \: + 6d \\ \\ given \: a + 6d = 154 \\ a = 154 - 6d$
Therefore, The first term of the given A. P is 154 - 6d