Fill in the blanks in the following table,given that $a$ is the first term,$d$ is the common difference,and $a_{n}$ is the $n^{th}$ term of the $AP$:
$S.No.$$a$$d$$n$$a_{n}$
$(i)$$7$$3$$8$$...$
$(ii)$$-18$$...$$10$$0$
$(iii)$$...$$-3$$18$$-5$
$(iv)$$-18.9$$2.5$$...$$3.6$
$(v)$$3.5$$0$$105$$...$

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) The general term of an $AP$ is given by the formula: $a_{n} = a + (n - 1)d$.
$(i)$ Given $a = 7, d = 3, n = 8$.
$a_{8} = 7 + (8 - 1)3 = 7 + (7)(3) = 7 + 21 = 28$.
$(ii)$ Given $a = -18, n = 10, a_{n} = 0$.
$0 = -18 + (10 - 1)d \rightarrow 18 = 9d \rightarrow d = 2$.
$(iii)$ Given $d = -3, n = 18, a_{n} = -5$.
$-5 = a + (18 - 1)(-3) \rightarrow -5 = a + (17)(-3) \rightarrow -5 = a - 51 \rightarrow a = 46$.
$(iv)$ Given $a = -18.9, d = 2.5, a_{n} = 3.6$.
$3.6 = -18.9 + (n - 1)2.5 \rightarrow 3.6 + 18.9 = (n - 1)2.5 \rightarrow 22.5 = (n - 1)2.5 \rightarrow n - 1 = 9 \rightarrow n = 10$.
$(v)$ Given $a = 3.5, d = 0, n = 105$.
$a_{105} = 3.5 + (105 - 1)0 = 3.5 + 0 = 3.5$.

Explore More

Similar Questions

The houses of a row are numbered consecutively from $1$ to $49$. Show that there is a value of $x$ such that the sum of the numbers of the houses preceding the house numbered $x$ is equal to the sum of the numbers of the houses following it. Find this value of $x$.

Difficult
View Solution

Find the $11^{th}$ term from the last term (towards the first term) of the $AP : 10, 7, 4, \ldots, -62$.

Difficult
View Solution

Find the sum of the first $24$ terms of the list of numbers whose $n^{th}$ term is given by $a_{n} = 3 + 2n$.

Find the $20^{th}$ term from the last term of the $AP : 3, 8, 13, \ldots, 253.$

Difficult
View Solution

In the following $APs,$ find the missing terms in the boxes: $\square, 38, \square, \square, \square, -22$

Difficult
View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo