Question

The first term of an AP is $-7$ and the common difference $5$, find its ${18}^{th}$ term and general term.
OR
Find the sum of first $22$ terms of an AP in which $d=7$ and ${22}^{nd}$ term is $149$.

Answer 1

${18}^{th}$ term fine

a= first term = -7 d= common diff = 5

general term

= a+(n-1)d

=-7+(18-1)5

=-7+85

= 78 Answer

II part

last term = 149 given in question

L = a+(n-1)d

149=a+(22-1)7

$149=a+21\times 7$

149=a+147

a=149-147

a=2

$S=\frac{n(a+L)}{2}$

$S=\frac{22(2+149)}{2}$

$S=\frac{22\left(151\right)}{2}$

Sum = 1661