Question

If the difference between the $7^{th}$ term and $2^{nd}$ term of an A.P. is 45 and $8^{th}$ term of the A.P is 67, find the sum of first 19 terms.

• A. 1615
• B. 1515
• C. 1655
• D. 1715

Answer 1

The correct option is A

1615

Let a be the first term and d be the common difference of the A.P.
a + 6d - (a+d) = 45.
5d =45
d = 9.
a + 7d = 67
a = 4
Sum of the first 19 terms = $\frac{19}{2}\left(\right(2\left)\right(4)+(18\left)\right(9\left)\right)$
=1615