This is an arithmetic progression based question from Chapter name- Arithmetic Progression
Chapter number- 9
Exercise – 9.6
In this question we have to find out which term of the A.P. -2, -7, -12,…, will be -77.
Also we have to find the sum of this A.P. up to the term -77.
CBSE DHANPAT RAI PUBLICATIONS
Understanding CBSE Mathematics
Class :- 10th
Question no 72
Given A.P. has first term(a) = –2, common difference(d) = –7 – (–2) = –5, and given term(an) = –77
Now, we know nth term of an A.P. is given by an = a + (n – 1)d.
=> –77 = –2 + (n – 1)(–5)
=> –5(n – 1) = –75
=> n – 1 = 15
=> n = 16
By using the formula of the sum of n terms of an A.P.
Sn = n[2a +(n – 1)d] / 2
So, sum up to the term –77 = S16
= 16[2(–2) + (16 – 1)(–5)]/2
= 8[–4 – 75]
= 8[–79]
= –632
Hence, 16th term of the A.P. will be –77 and sum up to this term is –632.