Find the sum of the first 25 terms of an A.P. whose nth term is given by $a_{n} = 7 - 3 n$ .

Open in App

Solution

Ln = 7 -3n ------(1)

$l_{1}$ = 7- 3 x 1 = 7-3 =4

$l_{2}$ = 7 - 3 x 2 = 7 - 6 =1

$l_{3}$ = 7 - 3 x 3 = 7 - 9 = -2

first term = a = 4

common difference = d = l2 - l1 = 1-4 = -3

sum of 25 terms = $s_{n}$ = n/2[2a+(n-1)d]

$s_{25}$ = 25/2 x [ 2 x 4 + (25-1)(-3)]
= 25/2 x [8 + 24(-3)]
= 25/2 x [ 8- 72]
= 25/2 x [-64]
= - 25 x 32
= -800

therefore
the sum of 25 terms in an AP is -800

Suggest Corrections

Similar questions

n^{t h}

T_{n} = (7 - 3 n)

Find the sum of first $24$ terms of the A.P. whose $n^{t h}$ term is given by $a_{n} = 3 + 2 n$

25

n^{t h}

a_{n}

= 2 - 3 n .

25

n

a_{n} = 2 - 3 n

Join BYJU'S Learning Program